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

TL;DR

This paper explores the geometric properties of lightlike hypersurfaces within $(\\epsilon)$-para Sasakian manifolds, introducing new classifications and analyzing their integrability conditions.

Contribution

It defines invariant and semi-invariant lightlike hypersurfaces in $(\epsilon)$-almost paracontact metric manifolds and investigates their integrability conditions in the specific case of $(\epsilon)$-para Sasakian manifolds.

Findings

Defined invariant and semi-invariant lightlike hypersurfaces

Provided examples of such hypersurfaces

Analyzed integrability conditions for distributions

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.