Search

We construct the M-Theory lifts of type IIA orientifolds based on K3-fibred Calabi-Yau threefolds with compatible involutions. Such orientifolds are shown to lift to M-Theory on twisted connected sum G2 manifolds. Beautifully, the two building blocks forming the G2 manifold correspond to the open and closed string sectors. As an application, we show how to use such lifts to explicitly study open string moduli. Finally, we use our analysis to construct examples of G2 manifolds with different inequivalent TCS realizations. [ABSTRACT FROM AUTHOR]

We show that, for a closed orientable n -manifold, with n not congruent to 3 modulo 4, the existence of a CR-regular embedding into complex (n − 1) -space ensures the existence of a totally real embedding into complex n -space. This implies that a closed orientable (4 k + 1) -manifold with non-vanishing Kervaire semi-characteristic possesses no CR-regular embedding into complex 4 k -space. We also pay special attention to the cases of CR-regular embeddings of spheres and of simply-connected 5-manifolds. [ABSTRACT FROM AUTHOR]

We construct globally-defined SU(3) structures on smooth compact toric varieties (SCTV) in the class of $$ \mathbb{C}{\mathrm{\mathbb{P}}}^1 $$ bundles over M , where M is an arbitrary SCTV of complex dimension two. The construction can be extended to the case where the base is Kähler-Einstein of positive curvature, but not necessarily toric, and admits a parameter space which includes SU(3) structures of LT type. [ABSTRACT FROM AUTHOR]

Label embedding (LE) is an important family of multi-label classification algorithms that digest the label information jointly for better performance. Different real-world applications evaluate performance by different cost functions of interest. Current LE algorithms often aim to optimize one specific cost function, but they can suffer from bad performance with respect to other cost functions. In this paper, we resolve the performance issue by proposing a novel cost-sensitive LE algorithm that takes the cost function of interest into account. The proposed algorithm, cost-sensitive label embedding with multidimensional scaling (CLEMS), approximates the cost information with the distances of the embedded vectors by using the classic multidimensional scaling approach for manifold learning. CLEMS is able to deal with both symmetric and asymmetric cost functions, and effectively makes cost-sensitive decisions by nearest-neighbor decoding within the embedded vectors. We derive theoretical results that justify how CLEMS achieves the desired cost-sensitivity. Furthermore, extensive experimental results demonstrate that CLEMS is significantly better than a wide spectrum of existing LE algorithms and state-of-the-art cost-sensitive algorithms across different cost functions. [ABSTRACT FROM AUTHOR]

For gradient-like flows without heteroclinic intersections of the stable and unstable manifolds of saddle periodic points all of whose saddle equilibrium states have Morse index 1 or n − 1, the notion of consistent equivalence of energy functions is introduced. It is shown that the consistent equivalence of energy functions is necessary and sufficient for topological equivalence. [ABSTRACT FROM AUTHOR]

In this paper, we study the rotationally invariant minimal surfaces in the Bao-Shen's spheres, which are a class of 3-spheres endowed with Randers metrics of constant flag curvature K = 1, where are Berger metrics, are one-forms and k > 1 is an arbitrary real number. We obtain a class of nontrivial minimal surfaces isometrically immersed in the Bao-Shen's spheres, which is the first class of nontrivial minimal surfaces with respect to the Busemann-Hausdorff measure in Finsler spheres. Moreover, we also obtain a new class of explicit minimal surfaces in the classical Berger spheres , which was expected to get in [F. Torralbo, Rotationally invariant constant mean curvature surfaces in homogeneous 3-manifolds, Differential Geom. Appl. 28(5) (2010) 593-607]. [ABSTRACT FROM AUTHOR]

We obtain all linear Chern number inequalities satisfied by any smooth complete intersection threefold with ample canonical bundle. [ABSTRACT FROM AUTHOR]

We consider translators on manifolds with singularities of the type of a transversal intersection of smooth manifolds. We give the definition of ellipticity of translators, prove the finiteness (Fredholm property) theorem, and establish an index formula for the case of point singularities. [ABSTRACT FROM AUTHOR]

Calabi-Yau manifolds are geometric objects of central importance in several branches of mathematics, including differential geometry, algebraic geometry, and mathematical physics. In this paper, we give a brief introduction to the subject aimed at a general mathematical audience and present some of our results that shed some light on the possible ways in which families of Calabi-Yau manifolds can degenerate. [ABSTRACT FROM AUTHOR]

In this paper, we will give some results on the classification of essential closed surfaces in the surface sum of product I-bundle of closed surfaces and some applications of these results. [ABSTRACT FROM AUTHOR]

We establish the leafwise intersection property for closed, coisotropic submanifolds in an exact symplectic manifold satisfying natural additional assumptions. [ABSTRACT FROM PUBLISHER]

We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward euclidean representation exists. In this paper, we propose using the properties of information geometry and statistical manifolds in order to define similarities between data sets using the Fisher information distance. We will show that this metric can be approximated using entirely nonparametric methods, as the parameterization and geometry of the manifold is generally unknown. Furthermore, by using multidimensional scaling methods, we are able to reconstruct the statistical manifold in a low-dimensional euclidean space; enabling effective learning on the data. As a whole, we refer to our framework as Fisher Information Nonparametric Embedding (FINE) and illustrate its uses on practical problems, including a biomedical application and document classification. [ABSTRACT FROM AUTHOR]

Abstract  Let E G be a holomorphic principal G-bundle over a compact connected Kähler manifold, where G is a connected complex reductive linear algebraic group. Consider a line bundle over E G /P corresponding to a character of P, where P is a parabolic subgroup of G. We give conditions for this holomorphic line bundle to be numerically effective. [ABSTRACT FROM AUTHOR]

We classify projective manifolds X of dimension n ≥ 3 with nef anticanonical class and index n – 1 such that . [ABSTRACT FROM AUTHOR]

Let M = Γ\G be a nilmanifold endowed with an invariant complex structure. We prove that Kuranishi deformations of abelian complex structures are all invariant complex structures, generalizing a result in [7] for 2-step nilmanifolds. We characterize small deformations that remain abelian. As an application, we observe that at real dimension six, the deformation process of abelian complex structures is stable within the class of nilpotent complex structures. We give an example to show that this property does not hold in higher dimension. [ABSTRACT FROM AUTHOR]

Abstract: We study conditions for the coexistence of singularities of a stable smooth mapping of a closed manifold into a manifold of the same dimension n. Assuming that this mapping has only singularities of corank 1, we find universal linear relations between the Euler characteristics of the manifolds of multi-singularities in the image of the considered mapping. To cite this article: V.D. Sedykh, C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]

A proof of the fact that the group $\backslash text\{\backslash rm\; Emb\}\_5(\{\backslash Bbb\; R\}^7)$ of cobordisms of embeddings of nonoriented 5-manifolds in $\{\backslash Bbb\; R\}^7$ is cyclic of order 6 is announced. A geometric description of a generator of this group is presented. Bibliography: 4 titles. [ABSTRACT FROM AUTHOR]

Abstract. A projective algebraic surface which is homeomorphic to a ruled surface over a curve of genus g≥1 is itself a ruled surface over a curve of genus g. In this note, we prove the analogous result for projective algebraic manifolds of dimension 4 in the case g≥2. [ABSTRACT FROM AUTHOR]

We develop the formulation of DFT on pre-QP-manifold. The consistency conditions like section condition and closure constraint are unified by a weak master equation. The Bianchi identities are also characterized by the pre-Bianchi identity. Then, the background metric and connections are formulated by using covariantized pre-QP-manifold. An application to the analysis of the DFT on group manifold is given. [ABSTRACT FROM AUTHOR]

Motivated by some results in classical differential geometry, we give a constructive procedure for building up a connection over a (twisted) tensor product of two algebras, starting from connections defined on the factors. The curvature for the product connection is explicitly calculated, and shown to be independent of the choice of the twisting map and the module twisting map used to define the product connection. As a consequence, we obtain that a product of two flat connections is again a flat connection. We show that our constructions also behave well with respect to bimodule structures, namely being the product of two bimodule connections again a bimodule connection. As an application of our theory, all the product connections on the quantum plane are computed. [ABSTRACT FROM PUBLISHER]