Half Lightlike Submanifolds of a Semi-Riemannian Manifold of Quasi-Constant Curvature

Abstract

We study the geometry of half lightlike submanifolds $(M, g, S(TM), S(TM^{\bot}))$ of a semi-Riemannian manifold $(\widetilde{M}, \widetilde{g})$ of quasi-constant curvature subject to the following conditions; (1) the curvature vector field $\zeta$ of $\widetilde{M}$ is tangent to $M$, (2) the screen distribution $S(TM)$ of $M$ is either totally geodesic or totally umbilical in $M$, and (3) the co-screen distribution $S(TM^{\bot})$ of $M$ is a conformal Killing distribution.