# 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.

## Key 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.