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

Abstract

We study the geometry of lightlike submanifolds $(M,g,S\left(TM\right),S\left(T{M}^{\perp }\right))$ of a semi-Riemannian manifold $\left(\tilde{M},\tilde{g}\right)$ of quasiconstant curvature subject to the following conditions: (1) the curvature vector field ζ of $\tilde{M}$ is tangent to $M$, (2) the screen distribution $S\left(TM\right)$ of $M$ is totally geodesic in $M$, and (3) the coscreen distribution $S\left(T{M}^{\perp }\right)$ of $M$ is a conformal Killing distribution.