Lightlike Submanifolds of a Semi-Riemannian Manifold With a Semi-Symmetric Non-Metric Connection

Abstract

We study lightlike submanifolds M of a semi-Riemannian manifoldM with a semi-symmetric non-metric connection subject to the conditions; (a) the characteristic vector field ofM is tangent to M , (b) the screen distribution on M is totally umbilical in M and (c) the co-screen distribution on M is conformal Killing.

Singular Theorems for Lightlike Submanifolds in a Semi-Riemannian Space Form

“…Theorem 2.2 [12]. Let M be an r-lightlike submanifold of a semi-Riemannian manifoldM admitting a semi-symmetric non-metric connection.…”

Einstein Lightlike Hypersurfaces of a Lorentz Space Form With a Semi-Symmetric Non-Metric Connection

“…Yasar, Cöken and Yücesan [12] and Jin [9] studied lightlike hypersurfaces in a semi-Riemannian manifold admitting a semi-symmetric non-metric connection. Recently Jin [8] studied lightlike submanifolds of a semi-Riemannian manifold with a semi-symmetric non-metric connection subject to the conditions; (a) the structure vector field of M belongs to the screen distribution S(T M ) and (b) S(T M ) is totally umbilical in M .…”

Two Characterization Theorems for Lightlike Hypersurfaces of a Semi-Riemannian Space Form

“…Although now we have lightlike version of a large variety of Riemannian submanifolds, the theory of lightlike submanifolds of semi-Riemannian manifolds with semisymmetric non-metric connections has been few known. Yasar et al [20] and Jin [11] ∼ [15] studied lightlike submanifolds of semi-Riemannian manifolds admitting semi-symmetric non-metric connections.…”