On the Geometry of Lightlike Hypersurfaces

Abstract

The study of lightlike geometry in semi-Riemannian manifolds was introduced by A. Bejancu and K. L. Duggal in their book [3]. The book laid a foundation for the study of lightlike submanifolds by providing some constructions on such subspaces. In this research, we focus on the study of lightlike hypersurfaces of semi-Riemannian manifolds, i.e. submanifolds of codimension one. In this line, we prove necessary and sufficient conditions for a lightlike hypersurface of a semi-Riemannian space form to be totally umbilical, screen conformal and screen almost conformal (see Theorem 2.5.2, 2.5.4 and 2.5.5)