Hypersurfaces of Lorentzian para-Sasakian manifolds

TL;DR

This paper explores the geometric properties of invariant and noninvariant hypersurfaces within Lorentzian para-Sasakian manifolds, establishing conditions for their structures and providing illustrative examples.

Contribution

It introduces new conditions for hypersurfaces to be locally product manifolds and establishes a Lorentzian para-Sasakian structure on invariant hypersurfaces.

Findings

Noninvariant hypersurfaces admit almost product structures.

Conditions for hypersurfaces to be locally product manifolds.

Examples illustrating invariant and noninvariant hypersurfaces.

Abstract

In this paper, we study the invariant and noninvariant hypersurfaces of (1,1,1) almost contact manifolds, Lorentzian almost paracontact manifolds and Lorentzian para-Sasakian manifolds, respectively. We show that a noninvariant hypersurface of an (1,1,1) almost contact manifold admits an almost product structure. We investigate hypersurfaces of affinely cosymplectic and normal (1,1,1) almost contact manifolds. It is proved that a noninvariant hypersurface of a Lorentzian almost paracontact manifold is an almost product metric manifold. Some necessary and sufficient conditions have been given for a noninvariant hypersurface of a Lorentzian para-Sasakian manifold to be locally product manifold. We establish a Lorentzian para-Sasakian structure for an invariant hypersurface of a Lorentzian para-Sasakian manifold. Finally we give some examples for invariant and noninvariant hypersurfaces of a Lorentzian para-Sasakian manifold.