Search

Let $\mathbb{F}$ be a field of characteristic $\neq 2$ and $3$, let $V$ be a $\mathbb{F}$-vector space of dimension $6$, and let $\Omega \in \wedge ^2V^\ast $ be a non-degenerate form. A system of generators for polynomial invariant functions under the tensorial action of the group $Sp(\Omega )$ on $\wedge ^3 V^\ast $, is given explicitly. Applications of these results to the normal forms of De Bruyn-Kwiatkowski and Popov are given., Comment: Preprint

We report dynamical mass measurements of the individual stars in the most luminous and massive stellar member of the nearby Ophiuchus star-forming region, the young tight binary system S1. We combine 28 archival datasets with seven recent, proprietary VLBA observations obtained as part of the \textit{Dynamical Masses of Young Stellar Multiple Systems with the VLBA} project (DYNAMO--VLBA), to constrain the astrometric and orbital parameters of the system, and recover high accuracy dynamical masses. The primary component, S1A, is found to have a mass of 4.11$\pm$0.10~M$_\odot$, significantly less than the typical value, $\sim$~6~M$_\odot$ previously reported in the literature. We show that the spectral energy distribution of S1A can be reproduced by a reddened blackbody with a temperature between roughly 14,000~K and 17,000~K. According to evolutionary models, this temperature range corresponds to stellar masses between 4~M$_\odot$ and 6~M$_\odot$ so the SED is not a priori inconsistent with the dynamical mass of S1A. The luminosity of S1 derived from SED-fitting, however, is only consistent with models for stellar masses above 5~M$_\odot$. Thus, we cannot reconcile the evolutionary models with the dynamical mass measurement of S1A: the models consistent with the location of S1A in the HR diagram correspond to masses at least 25\% higher than the dynamical mass. For the secondary component, S1B, a mass of 0.831~$\pm$~0.014~M$_\odot $ is determined, consistent with a low-mass young star. While the radio flux of S1A remains roughly constant throughout the orbit, the flux of S1B is found to be higher near the apastron.

We present a study of six dusty and gaseous pillars (containing the HH 1004 and HH 1010 objects) and globules (that contain the HH 666, HH 900, HH 1006, and HH 1066 objects) localized in the Carina nebula using sensitive and high angular resolution ($\sim$0.3$''$) Atacama Large Millimeter/Sub-millimeter Array (ALMA) observations. This is a more extensive study that the one presented in \citet{Cortes}. As in this former study, we also analyzed the 1.3 mm continuum emission and C$^{18}$O(2$-$1), N$_2$D$^+$(3$-$2) and $^{12}$CO(2$-$1) spectral lines. These new observations revealed the molecular outflows emanating from the pillars, the dusty envelopes$+$disks that are exciting them, and the extended HH objects far from their respective pillars. We reveal that the masses of the disks$+$envelopes are in a range of 0.02 to 0.38 M$_\odot$, and those for the molecular outflows are of the order of 10$^{-3}$ M$_\odot$, which suggests that their exciting sources might be low- or intermediate-mass protostars as already revealed in recent studies at infrared and submillimeter bands. In the regions associated with the objects HH 900 and HH 1004, we report multiple millimeter continuum sources, from where several molecular outflows emanate.

We present results from a sample of 106 high-luminosity IRAS sources observed with the Very Large Array in the B and C configurations. 96 sources were observed in the X-band and 52 in the K-band, with 42 of them observed at both wavelengths. We also used previously published observations in the C-band for 14 of them. The detection rate of sources with 3.6~cm continuum emission was $\sim25\%$, while only 10\% have emission at 1.3~cm. In order to investigate the nature of these sources, their physical parameters were calculated mainly using the 3.6~cm continuum emission, and for sources detected at two wavelengths, we used the best fit of three HII region models with different geometries. As a final result, we present a catalog of the detected sources, which includes their basic physical parameters for further analysis. The catalog contains 17 ultracompact HII regions and 3 compact HII regions., Comment: Accepted for publication in Revista Mexicana de Astronomia y Astrofisica (October 2023)

We report the detection of three compact ($< 0.001$ pc) radio sources (CRSs) at K$_{a}$-band (0.9 cm) in the \uchiirs G040.54+2.59 (two CRSs) and G034.13+0.47 (one CRS). These CRSs have weak flux densities and are located at the center of their respective \uchii regions. We found no clear association between massive ionizing stars and CRSs but some radiative influence on the latter, as suggested by their large emission measures (> $10^7 \mathrm{cm}^{-6}\mathrm{pc}$), typical of photo evaporating neutral objects close to or associated with massive stars. Our modelling of G40.54+2.59 shows that their CRSs supply enough ionized material to shape its morphology while significantly extending its observable lifetime. On the other hand, despite the possible relation of the CRS with the large-scale outflow signatures observed in G034.13+0.47, the influence of this CRS on the evolution of the \uchii region is unlikely. Our results show that the presence of CRSs can alleviate the so-called lifetime problem of UCHII regions. Still, to address their dynamical evolution adequately, the scenario must include additional mechanisms like ambient confinement, or the role of the kinematics of their associated stellar objects., Comment: Published in Publications of the Astronomical Society of Japan, Volume 75, Issue 1, February 2023, Pages 90-102, https://doi.org/10.1093/pasj/psac090

We present a catalog of radio sources of the M 17 region based on deep X band radio observations centered at 10 GHz obtained with the Jansky Very Large Array in the A configuration. We detect a total of 194 radio sources, 12 of them extended and 182 compact. We find that a significant fraction (at least 40% in our catalog) have suspected gyrosynchrotron emission associated with stellar coronal emission. By comparing the radio luminosities of our sources with their X ray counterparts, when available, we find that they are underluminous in X rays with respect to the G\"udel Benz relation, but a correlation with a similar slope is obtained provided that only sources with evident non thermal nature are selected from the sample compiled for the Orion Nebula Cluster (ONC) and M 17. The comparison of M 17 with the ONC and NGC 6334D-F leads to a similar luminosity function for the three regions, at least for the more luminous sources. However, the radio sources in M 17 are three times more numerous compared to the other regions at a given luminosity and their spatial distribution differs from that of Orion. Moreover, an arc-shaped structure of 40$"$ in extent is observed in our map, identified previously as an ionizing front, with the cometary Hyper Compact source UC1 at its focus. Archival 1 mm ALMA data reveals compact emission coincident with the radio wavelength peak, possibly associated with a protostellar disk of the massive star exciting UC1., Comment: 25 pages, 8 tables, 8 figures, accepted for publication in The Astronomical Journal

We observed H$_2$O (6$_{16}$ $\rightarrow$ 5$_{23}$) maser emission associated with the high-mass star-forming region IRAS 23139+5959 using the KaVA a combination of VLBI arrays between the KVN (Korea) and VERA (Japan). Through multi-epoch KaVA observations, we detected three groups of maser features, two of which coincide with those previously detected by the Karl G. Jansky Very Large Array (VLA). By determining the maser proper motions, we found that the first of maser groups exhibit an expanding motion that traces a wide-angle outflow almost along the line of sight, while the second one seems to be associated with the envelope of an \hii region. We discuss the star formation activity in IRAS 23139+5939, which may be reflected in the high variability of H$_2$O masers associated with an outflow seen from the front., Comment: 13 pages, 5 Figures, Published on Publications of the Astronomical Society of Japan, 2021

We present Very Large Array 7 mm continuum observations of four Ultra-Compact (UC)HII regions, observed previously at 1.3 cm, in order to investigate the nature of the compact radio sources associated with these regions. We detected a total of seven compact radio sources, four of them with thermal emission, and two compact radio sources have clear non-thermal emission. The thermal emission is consistent with the presence of an ionized envelope, either static (i.e., trapped in the gravitational radius of an associated massive star) or flowing away (i.e., a photo-evaporative flow). On the other hand, the nature of the non-thermal sources remains unclear and several possibilities are proposed. The possibility that most of these compact radio sources are photo-evaporating objects and the remaining ones more-evolved objects is consistent with previous studies on UCHII regions., Comment: 15 pages, 2 figures, 4 tables, accepted for publication in Revista Mexicana de Astronomia y Astrofisica

We present Atacama Large Millimeter/Submillimeter Array (ALMA) 1.3 mm continuum and C$^{18}$O(2$-$1), N$_2$D$^{+}$(3$-$2), $^{13}$CS(5$-$4), and $^{12}$CO(2$-$1) line sensitive and high angular resolution ($\sim$0.3$''$) observations of the famous carina pillars and protostellar objects HH 901/902. Our observations reveal for the first time, the bipolar CO outflows and the dusty disks (plus envelopes) that are energizing the extended and irradiated HH objects far from the pillars. We find that the masses of the disks$+$envelopes are about 0.1 M$_\odot$ and of the bipolar outflows are between 10$^{-3}$ - 10$^{-4}$ M$_\odot$, which suggests that they could be low- or maybe intermediate- mass protostars. Moreover, we suggest that these young low-mass stars are likely embedded Class 0/I protostars with high-accretion rates. We also show the kinematics of the gas in the pillars together with their respective gas masses (0.1 -- 0.2 M$_\odot$). We estimate that the pillars will be photo-evaporated in 10$^4$ to 10$^5$ years by the massive and luminous stars located in the Trumpler 14 cluster. Finally, given the short photo-evaporated timescales and that the protostars in these pillars are still very embedded, we suggest that the disks inside of the pillars will be quickly affected by the radiation of the massive stars, forming proplyds, like those observed in Orion., Comment: Accepted to The Astronomical Journal

The theory of gauge fields in Theoretical Physics poses several mathematical problems of interest in Differential Geometry and in Field Theory. Below we tackle one of these problems: The existence of a finite system of generators of gauge-invariant Lagrangians and how to compute them. More precisely, if $p\colon C\to M$ is the bundle of connections on a principal $G$-bundle $\pi\colon P\to M$, then a finite number $L_1,\dotsc,L_{N^\prime }$ of gauge-invariant Lagrangians defined on $J^1C$ is proved to exist such that for any other gauge-invariant Lagrangian $L\in C^\infty (J^1C)$ there exists a function $F\in C^\infty (\mathbb{R}^{N^\prime })$ such that $L=F(L_1,\dotsc,L_{N^\prime})$. Several examples are dealt with explicitly.

Let $\mathbb{F}$ be a field of characteristic different from $2$ and $3$, and let $V$ be a vector space of dimension $2$ over $\mathbb{F}$. The generic classification of homogeneous quadratic maps $f\colon V\to V$ under the action of the linear group of $V$, is given and efficient computational criteria to recognize equivalence are provided., Comment: 12 pages, no figures

Let $M$ be a smooth manifold of dimension $2n$, and let $O_{M}$ be the dense open subbundle in $\wedge^{2}T^{\ast}M$ of $2$-covectors of maximal rank. The algebra of $\operatorname*{Diff}M$-invariant smooth functions of first order on $O_{M}$ is proved to be isomorphic to the algebra of smooth $Sp(\Omega_{x})$-invariant functions on $\wedge^{3}T_{x}^{\ast}M$, $x$ being a fixed point in $M$, and $\Omega_{x}$ a fixed element in $(O_{M})_{x}$. The maximum number of functionally independent invariants is computed.

We report continuum GMRT observations aimed to explore the behavior of the jet associated with IRAS 16547-4247 at very low frequencies (325 MHz and 610 MHz). The obtained maps reveal an elongated morphology in the SE-NW direction. In addition, the 610 MHz map shows three knots associated to the elongated morphology that seems to correspond to the triple radio source identified as the jet seen at higher frequencies. However, at 325 MHz, although an elongated morphology is also observed, only two knots appear in the map. By comparing our knot positions at both frequencies with a precessing jet model used in a previous work, we find that the knots fall closely to the wiggling path and, hence, they likely represent shocks of the material of the precessing jet with the medium. Only the nature of the southernmost knot detected at 325 MHz remains unclear. Besides, we found that the whole emission of the lobes is non-thermal down to very low frequencies and that the possible associated emission mechanisms work differently in in both lobes, causing the discrepancies between observed frequencies. To explain these discrepancies we investigate mechanisms such as synchrotron radiative losses in a magnetic field of about 0.5 mG in the shocks and find this possibility unlikely to occur. Alternatively, we invoke interaction with an inhomogeneous medium as the most probable scenario., Comment: 12 pages, 4 Figures, 3 Tables; accepted for publication in MNRAS

A method is obtained to compute the maximum number of functionally independent invariant functions under the action of a linear algebraic group as long as its Lie algebra admits a base of square-zero matrices. Some applications are also given.

An intrinsic description of the Hamilton-Cartan formalism for first-order Berezinian variational problems determined by a submersion of supermanifolds is given. This is achieved by studying the associated higher-order graded variational problem through the Poincar\'e-Cartan form. Noether theorem and examples from superfield theory and supermechanics are also discussed., Comment: Already published. Placed here for archiving purposes

We study the relation between the Laplacian associated to an odd metric on a supermanifold and harmonic superfunctions, through the application of the calculus of variations to a supersymmetric sigma model., Comment: Already published. Placed here for archiving purposes

The notion of type of a differential 2-form in four variables is introduced and for 2-forms of type < 4, local normal models are given. If the type of a 2-form $\Omega$ is 4, then the equivalence under diffeomorphisms of $\Omega$ is reduced to the equivalence of a symplectic linear frame functorially attached to $\Omega$. As the equivalence problem for linear parallelisms is known, the present work solves generically the equivalence problem under diffeomorphisms of germs of 2-forms in 4 variables., Comment: 16 pages

We present a new group law defined on a subset of the projective plane $\mathbb{F}P^2$ over an arbitrary field $\mathbb{F}$, which lends itself to applications in Public Key Cryptography, in particular to a Diffie-Hellman-like key agreement protocol. We analyze the computational difficulty of solving the mathematical problem underlying the proposed Abelian group law and we prove that the security of our proposal is equivalent to the discrete logarithm problem in the multiplicative group of the cubic extension of the finite field considered. Finally, we present a variant of the proposed group law but over the ring $\mathbb{Z}/pq\mathbb{Z}$, and explain how the security becomes enhanced, though at the cost of a longer key length., Comment: * Updated abstract. * Updated security considerations in section 3. * Added brand new section 4, considering an analogous cryptosystem over a ring, thus adding security. * Update conclusions, taking the new section into account. * Updated references. * Corrected typos

We present sensitive high angular resolution ($\sim$ 0.1$''$ -- 0.3$''$) continuum ALMA (The Atacama Large Millimeter/Submillimeter Array) observations of the archetypal hot core located in Orion-KL. The observations were made in five different spectral bands (bands 3, 6, 7, 8, and 9) covering a very broad range of frequencies (149 -- 658 GHz). Apart of the well-know millimeter emitting objects located in this region (Orion Source I and BN), we report the first submillimeter detection of three compact continuum sources (ALMA 1-3) in the vicinities of the Orion-KL hot molecular core. These three continuum objects have spectral indices between 1.47 to 1.56, and brightness temperatures between 100 to 200 K at 658 GHz suggesting that we are seeing moderate optically thick dust emission with possible grain growth. However, as these objects are not associated with warm molecular gas, and some of them are farther out from the molecular core, we thus conclude that they cannot heat the molecular core. This result favours the hypothesis that the hot molecular core in Orion-KL core is heated externally., Comment: Accepted to ApJ

Let $M$ be a connected smooth manifold, let $\operatorname{Aut}(p)$ be the group automorphisms of the bundle $p\colon \mathbb{R}\times M\to \mathbb{R}$, and let $q\colon J^1(\mathbb{R},M)\times \mathbb{R\to }J^1(\mathbb{R},M)$ be the canonical projection. Invariant functions on $J^r(q)$ under the natural action of $\operatorname{Aut}(p)$ are discussed in relationship with the Lagrangian equivalence problem. The second-order invariants are determined geometrically as well as some other higher-order invariants for $\dim M\geq 2$.

Ultra-Compact (UC)HII regions represent a very early stage of massive star formation whose structure and evolution are not yet fully understood. Interferometric observations in recent years show that some UCHII regions have associated compact sources of uncertain nature. Based on this, we carried out VLA 1.3 cm observations in the A configuration of selected UCHII regions in order to report additional cases of compact sources embedded in UCHII regions. From the observations, we find 13 compact sources associated to 9 UCHII regions. Although we cannot establish an unambiguous nature for the newly detected sources, we assess some of their observational properties. According to the results, we can distinguish between two types of compact sources. One type corresponds to sources that probably are deeply embedded in the dense ionized gas of the UCHII region. These sources are being photo-evaporated by the exciting star of the region and will last for 10$^4-10^5$ yr. They may play a crucial role in the evolution of the UCHII region as the photo-evaporated material could replenish the expanding plasma and might provide a solution to the so-called lifetime problem for these regions. The second type of compact sources is not associated with the densest ionized gas of the region. A few of these sources appear resolved and may be photo-evaporating objects such as those of the first type but with significantly lower mass depletion rates. The rest of sources of this second type appear unresolved and their properties are varied. We speculate on the similarity between the sources of the second type and those of the Orion population of radio sources., Comment: 33 pages, 6 figures, 4 tables. Accepted for publication in ApJ

(abridged) The HH 80/81/80N jet extends from the HH 80 object to the recently discovered Source 34 and has a total projected jet size of 10.3 pc, constituting the largest collimated radio-jet system known so far. It is powered by IRAS 18162-2048 associated with a massive young stellar object. We report 6 cm JVLA observations that, compared with previous 6 cm VLA observations carried out in 1989, allow us to derive proper motions of the HH 80, HH 81 and HH 80N radio knots located about 2.5 pc away in projection from the powering source. For the first time, we measure proper motions of the optically obscured HH 80N object providing evidence that HH 81, 80 and 80N are associated with the same radio-jet. We derived tangential velocities of these HH objects between 260 and 350 km/s, significantly lower than those for the radio knots of the jet close to the powering source (600-1400 km/s) derived in a previous work, suggesting that the jet material is slowing down due to a strong interaction with the ambient medium. The HH 80 and HH 80N emission at 6 cm is, at least in part, probably synchrotron radiation produced by relativistic electrons in a magnetic field of 1 mG. If these electrons are accelerated in a reverse adiabatic shock, we estimate a jet total density of $\lesssim1000$ cm$^{-3}$. All these features are consistent with a jet emanating from a high mass protostar and make evident its capability of accelerating particles up to relativistic velocities., Comment: 15 pages, 3 figures, 1 table, accepted for publication in ApJ

Second-order Lagrangian densities admitting a first-order Hamiltonian formalism are studied; namely, i) for each second-order Lagrangian density on an arbitrary fibred manifold $p\colon E\to N$ the Poincar\'e-Cartan form of which is projectable onto $J^1E$, by using a new notion of regularity previously introduced, a first-order Hamiltonian formalism is developed for such a class of variational problems; ii) the existence of first-order equivalent Lagrangians are discussed from a local point of view as well as global; iii) this formalism is then applied to classical Einstein-Hilbert Lagrangian and a generalization of the BF theory. The results suggest that the class of problems studied is a natural variational setting for GR.

We analyze high-resolution Very Large Array and Jansky Very Large Array continuum observations of the M8 region carried out at several epochs that span a period of 30 yr. Our maps reveal two compact sources. One is associated with Her 36 SE, a possible companion of the O7 luminous massive star Her 36, and the other is associated to G5.97-1.17, whose proplyd nature was previously established. With the analyzed data, we do not find significant time variability in any of these sources. The derived spectral index of $\ge 0.1$ for Her~36 SE, the marginal offset of the radio emission with the previous IR detection and the associated X-ray emission previously reported suggest the presence of an unresolved interaction region between the strong winds of Her~36 and Her~36 SE. This region would produce non-thermal contamination to the global wind emission of Her~36 flattening its spectral index. On the other hand, the emission of G5.97-1.17 can be also explained by a mixture of thermal and non-thermal emission components, with different relative contribution of both emission mechanisms along the proplyd. We argue that the shock created by the photo-evaporation flow of the proplyd with the collimated stellar wind of Her~36 accelerates charged particles in G5.97-1.17 producing considerable synchrotron emission. On the contrary, an electron density enhancement at the southwest of G5.97-1.17 makes the thermal emission dominant over this region., Comment: 19 pages, 3 figures, 3 tables, accepted for publication in ApJ

A handful of HII regions are known to exhibit a compact radio source near their centers. The nature of these compact radio sources is not well established. We present the analysis of new as well as archival Very Large Array observations of the compact source projected near the center of the NGC 6334A HII region, part of the NGC 6334 complex. We show that the compact source is time variable on a scale of years and determine for one epoch a non-thermal spectrum, suggestive of synchrotron emission. We propose that this source could be the wind interaction region of a massive binary system that could be the ionizing source of NGC 6334A., Comment: 4 pages, 3 figures, accepted for publication in Revista Mexicana de Astronomia y Astrofisica

We present VLA NH3 and PdBI NH2D and H13NC observations of the star forming core ahead of HH 80N, the optically obscured northern counterpart of the Herbig-Haro objects HH 80/81. The main goal is to determine the kinematical information of the high density regions of the core ($n\lesssim 10^5$ cm$^{-3}$), missed in previous works due to the depletion of the species observed (e.g. CS). The obtained maps show different kinematical signatures between the eastern and western parts of the core, suggesting a possible dynamical interaction of the core with the HH 80/81/80N outflow. The analysis of the Position-Velocity (PV) plots of these species rules out a previous interpretation of having a molecular ring-like structure of $6\times 10^4$ AU of radius traced by CS infalling onto a central protostar found in the core (IRS1). High degree of deuteration, with respect to the central part of the core harboring IRS1, is derived in the eastern part, where a dust condensation (SE) is located. This deuteration trend of NH3 suggests that SE is in a prestellar evolutionary stage, earlier than that of the IRS1. Since SE is the closest condensation to the HH 80N/81/80N outflow, in case of having outflow-core dynamical interaction, it should be perturbed first and be the most evolved condensation in the core. Therefore, the derived evolutionary sequence for SE and IRS1 makes the outflow triggered star formation on IRS1 unlikely., Comment: 19 pages, 5 figures, 2 tables, accepted for publication in ApJ

A first-order Lagrangian $L^\nabla $ variationally equivalent to the second-order Einstein-Hilbert Lagrangian is introduced. Such a Lagrangian depends on a symmetric linear connection, but the dependence is covariant under diffeomorphisms. The variational problem defined by $L^\nabla $ is proved to be regular and its Hamiltonian formulation is studied, including its covariant Hamiltonian attached to $\nabla $.

We present 6 and 20 cm JVLA/VLA observations of the northern head of the HH 80/81/80N jet, one of the largest collimated jet systems known so far, aimed to look for knots further away than HH 80N, the northern head of the jet. Aligned with the jet and 10 arcmin northeast of HH 80N, we found a radio source not reported before, with a negative spectral index similar to that HH 80, HH 81 and HH 80N. The fit of a precessing jet model to the knots of the HH 80/81/80N jet, including the new source, shows that the position of this source is close to the jet path resulting from the modeling. If the new source belongs to the HH 80/81/80N jet, its derived size and dynamical age are 18.4 pc and >9000 yr, respectively. If the jet is symmetric, its southern lobe would expand beyond the cloud edge resulting in an asymmetric appearance of the jet. Based on the updated dynamical age, we speculate on the possibility that the HH 80/81/80N jet triggered the star formation observed in a dense core found ahead of HH 80N, which shows signposts of interaction with the jet. These results indicate that pc scale radio jets can play a role on the stability of dense clumps and the regulation of star formation in the molecular cloud., Comment: 11 pages, 2 figures, 2 tables, accepted for publication in ApJL

The equivalence problem of curves with values in a Riemannian manifold, is solved. The domain of validity of Frenet's theorem is shown to be the spaces of constant curvature. For a general Riemannian manifold new invariants must thus be added. There are two important generic classes of curves; namely, Frenet curves and a new class, called curves "in normal position". They coincide in dimensions $\leq 4$ only. A sharp bound for asymptotic stability of differential invariants is obtained, the complete systems of invariants are characterized, and a procedure of generation is presented. Different classes of examples (specially in low dimensions) are analyzed in detail.

To each second-order ordinary differential equation $\sigma $ on a smooth manifold $M$ a $G$-structure $P^\sigma $ on $J^1(\mathbb{R},M)$ is associated and the Chern connection $\nabla ^\sigma $ attached to $\sigma $ is proved to be reducible to $P^\sigma $; in fact, $P^\sigma $ coincides generically with the holonomy bundle of $\nabla ^\sigma $. The cases of unimodular and orthogonal holonomy are also dealt with. Two characterizations of the Chern connection are given: The first one in terms of the corresponding covariant derivative and the second one as the only principal connection on $P^\sigma $ with prescribed torsion tensor field. The properties of the curvature tensor field of $\nabla ^\sigma $ in relationship to the existence of special coordinate systems for $\sigma $ are studied. Moreover, all the odd-degree characterictic classes on $P^\sigma $ are seen to be exact and the usual characteristic classes induced by $\nabla ^\sigma $ determine the Chern classes of $M$. The maximal group of automorphisms of the projection $p\colon \mathbb{R}\times M\to \mathbb{R}$ with respect to which $\nabla ^\sigma $ has a functorial behaviour, is proved to be the group of $p$-vertical automorphisms. The notion of a differential invariant under such a group is defined and stated that second-order differential invariants factor through the curvature mapping; a structure is thus established for KCC theory.

The Pipe nebula is a massive, nearby, filamentary dark molecular cloud with a low star-formation efficiency threaded by a uniform magnetic field perpendicular to its main axis. It harbors more than a hundred, mostly quiescent, very chemically young starless cores. The cloud is, therefore, a good laboratory to study the earliest stages of the star-formation process. We aim to investigate the primordial conditions and the relation among physical, chemical, and magnetic properties in the evolution of low-mass starless cores. We used the IRAM 30-m telescope to map the 1.2 mm dust continuum emission of five new starless cores, which are in good agreement with previous visual extinction maps. For the sample of nine cores, which includes the four cores studied in a previous work, we derived a Av to NH2 factor of (1.27$\pm$0.12)$\times10^{-21}$ mag cm$^{2}$ and a background visual extinction of ~6.7 mag possibly arising from the cloud material. We derived an average core diameter of ~0.08 pc, density of ~10$^5$ cm$^{-3}$, and mass of ~1.7 Msun. Several trends seem to exist related to increasing core density: (i) diameter seems to shrink, (ii) mass seems to increase, and (iii) chemistry tends to be richer. No correlation is found between the direction of the surrounding diffuse medium magnetic field and the projected orientation of the cores, suggesting that large scale magnetic fields seem to play a secondary role in shaping the cores. The full abstract is available in the pdf., Comment: 19 pages, 12 figures, 13 tables, accepted for publication in ApJ

We present a study of dense molecular gas kinematics in seventeen nearby protostellar systems using single-dish and interferometric molecular line observations. The non-axisymmetric envelopes around a sample of Class 0/I protostars were mapped in the N2H+ (J=1-0) tracer with the IRAM 30m, CARMA and PdBI as well as NH3 (1,1) with the VLA. The molecular line emission is used to construct line-center velocity and linewidth maps for all sources to examine the kinematic structure in the envelopes on spatial scales from 0.1 pc to ~1000 AU. The direction of the large-scale velocity gradients from single-dish mapping is within 45 degrees of normal to the outflow axis in more than half the sample. Furthermore, the velocity gradients are often quite substantial, the average being ~2.3 km\s\pc. The interferometric data often reveal small-scale velocity structure, departing from the more gradual large-scale velocity gradients. In some cases, this likely indicates accelerating infall and/or rotational spin-up in the inner envelope; the median velocity gradient from the interferometric data is ~10.7 km/s/pc. In two systems, we detect high-velocity HCO+ (J=1-0) emission inside the highest-velocity \nthp\ emission. This enables us to study the infall and rotation close to the disk and estimate the central object masses. The velocity fields observed on large and small-scales are more complex than would be expected from rotation alone, suggesting that complex envelope structure enables other dynamical processes (i.e. infall) to affect the velocity field., Comment: 85 Pages, 31 Figures, 11 Tables, Accepted to ApJS