Lightlike Hypersurfaces in Semi-Riemmanian Manifolds Admitting Affine Conformal Vector Fields

Abstract

Lightlike hypersurfaces with integrable screen distributions are very important as far as lightlike geometry is concerned. They include, among others, screen conformal and screen totally umbilic ones. In this paper, we show that any lightlike hypersurface of a semi-Riemannian manifold admitting a certain closed affine conformal vector field has an integrable screen distribution. Several examples are furnished in support of the main results.