Lightlike hypersurfaces in semi-Riemannian manifold with semi-symmetric non-metric connection

Abstract

In this paper, we study lightlike hypersurfaces of a semi-Riemannian manifold admitting a semisymmetric non-metric connection. We give the equations of Gauss and Codazzi. Then, we obtain conditions under which the Ricci tensor of a lightlike hypersurface is symmetric given that the ambient space is equipped with a semi-symmetric non-metric connection.

Lightlike Hypersurfaces of a Lorentz Manifold With a Semi-Symmetric Non-Metric Connection

“…In [2], they gave basic properties of submanifolds of a Riemannian manifold endowed with a semi-symmetric non-metric connection. Yasar, Cöken and Yücesan [6] studied lightlike hypersurfaces in a semi-Riemannian manifold endowed with a semi-symmetric non-metric connection. They found the condition that the Ricci type tensor of a lightlike hypersurface of such a semi-Riemannian manifold be symmetric.…”

Ascreen Lightlike Hypersurfaces of a Semi-Riemannian Space Form With a Semi-Symmetric Non-Metric Connection

“…Recently several authors ( [9]- [13]) studied lightlike hypersurfaces in a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. Most of authors that wrote on either lightlike hypersurfaces M of semi-Riemannian manifolds M admitting semi-symmetric non-metric connections or lightlike hypersurfaces M of indefinite almost contact manifolds M fail to treat with the case the structure vector field ζ of M is not tangent to M , but studied only to the case ζ is tangent to M (such M is called tangential lightlike submanifold ([9]- [13]) of M ). There are few papers on non-tangential lightlike submanifolds of indefinite almost contact manifolds studied by Jin ([6]- [8]).…”

Half Lightlike Submanifolds of a Semi-Riemannian Space Form With a Semi-Symmetric Non-Metric Connection

“…Although now we have lightlike version of a large variety of Riemannian submanifolds, the geometry of lightlike submanifolds of semi-Riemannian manifolds admitting semi-symmetric non-metric connections has been few known. Recently Yasar, Cöken and Yücesan [15] and Jin [6,7] studied lightlike hypersurfaces in a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. Jin [10] and Jin-Lee [11] studied general lightlike submanifolds and half lightlike submanifolds of a semi-Riemannian manifold with a semi-symmetric non-metric connection.…”