We study the forms of curvatures of lightlike hypersurfaces M of an indefinite Kenmotsu manifold M̄ subject to the conditions: (1) M is locally symmetric, i.e., the curvature tensor R of M be parallel on TM , or (2) M is a semi-symmetric manifold, i.e., R(X, Y )R = 0 on TM . M.S.C. 2010: 53C25, 53C40, 53C50.

In this paper we introduce the concept of (ε)-almost paracontact manifolds, and in particular, of (ε)-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of (ε)-para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it can not admit an (ε...

In Riemannian geometry geodesics are integral curves of the distance gradient. We extend this classical result to framework Information Geometry. particular, we prove that rays level-sets defined by a pseudo-distance generated sum two tangent vectors. By relying on these vectors, propose novel definition canonical divergence and its dual function. new allows recover given structure $$(\mathrm{g...

The object of the present paper is to study Z-symmetric manifold with projective curvature tensor. At first, we case Z-tensor and Ricci tensor being Codazzi type. Next, consider recurrent We also divergence-free Z-tensor. Finally, construct an example

In this study, we investigate the differential geometry of contact pseudo-slant submanifolds a (LCS)n -manifold. The necessary and sufficient conditions for (LCS)n-manifold are given.

Riemannian and pseudo-Riemannian symmetric spaces with semisimple transvection group are known and classified for a long time. Contrary to that the description of pseudo-Riemannian symmetric spaces with non-semisimple transvection group is an open problem. In the last years some progress on this problem was achieved. In this article we want to explain these results and some of their applications.