Lightlike hypersurfaces of an $(\epsilon)$-para Sasakian manifold

Abstract

In this paper, we initiate the study of lightlike hypersurfaces of an $(\epsilon)$-almost paracontact metric manifold which are tangent to the structure vector field. In particular, we give definitions of invariant lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces, and give some examples. Integrability conditions for the distributions involved in the screen semi-invariant lightlike hypersurface are investigated when the ambient manifold is an $(\epsilon)$-para Sasakian manifold.