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In this paper, we give a full classification of the separable hypersurfaces of constant sectional curvature in the Euclidean $n$-space $\mathbb{R}^n$. In dimension $n=3$, this classification was solved by Hasanis and L\'opez [Manuscripta Math. 166, 403-417 (2021)]. When $n>3$, we prove that the separable hypersurfaces of null sectional curvature are three particular families of such hypersurfaces. Finally, we prove that hyperspheres are the only separable hypersurfaces with nonzero constant sectional curvature., Comment: Your comments are welcome. 21 pages

We use the transverse K\"ahler-Ricci flow on the canonical foliation of a closed Vaisman manifold to deform the Vaisman metric into another Vaisman metric with a transverse K\"ahler-Einstein structure. We also study the main features of such a manifold. Among other results, using techniques from the theory of parabolic equations, we obtain a direct proof for the short time existence of the solution for transverse {\K}-Ricci flow on Vaisman manifolds, recovering in a particular setting a result of Bedulli, He and Vezzoni [J. Geom. Anal. 28, 697--725 (2018)], but without employing the Molino structure theorem. Moreover, we investigate Einstein-Weyl structures in the setting of Vaisman manifolds and find their relationship with quasi-Einstein metrics. Some examples are also provided to illustrate the main results., Comment: 26 pages

In this paper we investigate the possibility to obtain locally new Sasaki-Einstein metrics on the space $T^{1,1}$ considering a deformation of the standard metric tensor field. We show that from the geometric point of view this deformation leaves transverse and the leafwise metric intact, but changes the orthogonal complement of the Reeb vector field using a particular basic function. In particular, the family of metric obtained using this method can be regarded as solutions of the equation associated to the Sasaki-Ricci flow on the underlying manifold., Comment: 19 pages, references added, typos fixed

The main purpose of the present work is to investigate statistical manifolds endowed with almost product structures. We prove that the statistical structure of a para-K\"{a}hler-like statistical manifold of constant curvature in the Kurose's sense is a Hessian structure. We also derive the main properties of statistical submersions which are compatible with almost product structures. The results are illustrated by several nontrivial examples., Comment: 17 pages; minor corrections; to appear in "Bulletin des Sciences Math\'ematiques"

In this paper, we give an algorithm to infer the positions of the vertices of an unknown tetrahedron, given a sample of points which are uniformly distributed within the tetrahedron. The accuracy of the algorithm is demonstrated using some numerical experiments., Comment: 15 pages; version accepted for publication in Annali di Matematica Pura ed Applicata

In this article we obtain classification results on the quasi-product production functions in terms of the geometry of their associated graph hypersurfaces, generalizing in a new setting some recent results concerning basic production models. In particular, we obtain several results on the geometry of Spillman-Mitscherlich and transcendental production functions.

In the present paper we show that the complete list of special Killing forms on the 5-dimensional Sasaki-Einstein spaces $Y^{p,q}$ can be extracted using the symplectic potential and the classical Delzant construction. The results achieved here agree with previous ones obtained by direct computation, proving the reliability of the method which stands in fact as a general algorithm for toric Sasaki-Einstein manifolds. Finally, we discuss the integrability of geodesic motion in $Y^{p,q}$ spaces., Comment: 20 pages. arXiv admin note: text overlap with arXiv:1503.00443

Throughout this paper we investigate the complex structure of the conifold $C(T^{1,1})$ basically making use of the interplay between symplectic and complex approaches of the K\"{a}hler toric manifolds. The description of the Calabi-Yau manifold $C(T^{1,1})$ using toric data allows us to write explicitly the complex coordinates and apply standard methods for extracting special Killing forms on the base manifold. As an outcome, we obtain the complete set of special Killing forms on the five-dimensional Sasaki-Einstein space $T^{1,1}$., Comment: 17 pages

In this paper we prove two sharp inequalities involving the normalized scalar curvature and the generalized normalized $\delta$-Casorati curvatures for slant submanifolds in quaternionic space forms. We also characterize those submanifolds for which the equality cases hold. These results are a generalization of some recent results concerning the Casorati curvature for a slant submanifold in a quaternionic space form obtained by Slesar et al.: J. Inequal. Appl. 2014, 2014:123., Comment: 10 pages

In this note we classify quasi-sum production functions with constant elasticity of production with respect to any factor of production and with proportional marginal rate of substitution., Comment: 6 pages; minor changes and text improvements; references updated

In this paper we study the interplay between complex coordinates on the Calabi-Yau metric cone and the special Killing forms on the toric Sasaki-Einstein manifold. In the general case we give a procedure to locally construct the special Killing forms. In the final part we exemplify the general scheme in the case of the $5-$dimensional $Y^{p,q}$ spaces, identifying the additional special Killing 2-forms which were previously obtained by the second author of the present paper, but with a different method, in [Mod. Phys. Lett. A 27 (2012) 1250217]., Comment: 15 pages, version accepted for publication in Physica Scripta

In this paper, we completely classify homogeneous production functions with an arbitrary number of inputs whose production hypersurfaces are flat. As an immediate consequence, we obtain a complete classification of homogeneous production functions with two inputs whose production surfaces are developable., Comment: 11 pages; To appear in Applied Mathematics and Computation

We study the interplay between basic Dirac operator and transverse Killing and twistor spinors. In order to obtain results for general Riemannian foliations with bundle-like metric we consider transverse Killing spinors that appear as natural extension of the harmonic spinors associated with the basic Dirac operator. In the case of foliations with basic-harmonic mean curvature it turns out that these Killing spinors and twistor spinors coincide with the standard definition. We obtain the corresponding version of classical results on closed Riemannian manifold with spin structure, extending some previous results., Comment: updating version as accepted by Rev. Math. Phys

The hidden symmetries of higher dimensional Kerr-NUT-(A)dS metrics are investigated. In certain scaling limits these metrics are related to the Einstein-Sasaki ones. The complete set of Killing-Yano tensors of the Einstein-Sasaki spaces are presented. For this purpose the Killing forms of the Calabi-Yau cone over the Einstein-Sasaki manifold are constructed. Two new Killing forms on Einstein-Sasaki manifolds are identified associated with the complex volume form of the cone manifolds. Finally the Killing forms on mixed 3-Sasaki manifolds are briefly described., Comment: 15 pages; text revised in Section 3.2, references added

The purpose of this paper is to study the canonical totally real foliations of CR-submanifolds in a locally conformal K\"{a}hler manifold., Comment: 10 pages, Journal of Geometry and Physics (to appear)

In this paper we establish some inequalities concerning the $k$-Ricci curvature of a slant submanifold in a quaternionic space form. We also obtain obstructions to the existence of quaternionic slant immersions in quaternionic space forms with unfull first normal bundle., Comment: Accepted for publication in Publicationes Mathematicae Debrecen

In this paper we obtain several curvature properties of the twistor and reflector spaces of a paraquaternionic K\"{a}hler manifold and prove the existence of both positive and negative mixed 3-Sasakian structures in a principal SO(2,1)-bundle over a paraquaternionic K\"{a}hler manifold.

In this paper we study 3-submersions from a QR-hypersurface of a quaternionic Kaehler manifold onto an almost quaternionic hermitian manifold. We also prove the non-existence of quaternionic submersions between quaternionic Kaehler manifolds which are not locally hyper-Kaehler.

In this paper we obtain the structure equation of a contact-complex Riemannian submersion and give some applications of this equation in the study of almost cosymplectic manifolds with Kaehler fibres., Comment: Abh. Math. Semin. Univ. Hamb., to appear

Mixed 3-structures are odd-dimensional analogues of paraquaternionic structures. They appear naturally on lightlike hypersurfaces of almost paraquaternionic hermitian manifolds. We study invariant and anti-invariant submanifolds in a manifold endowed with a mixed 3-structure and a compatible (semi-Riemannian) metric. Particular attention is given to two cases of ambient space: mixed 3-Sasakian and mixed 3-cosymplectic., Comment: to appear in Mediterr. J. Math. 9 (2012), no. 2