Slant and Semi-Slant Submanifolds of a Lorentzian Almost Paracontact Manifold

TL;DR

This paper introduces and analyzes the properties of slant and semi-slant submanifolds within Lorentzian almost paracontact manifolds, providing conditions for their characterization and examples.

Contribution

It establishes necessary and sufficient conditions for slant submanifolds and explores integrability conditions in specific Lorentzian manifold settings.

Findings

Derived conditions for slant submanifolds

Provided examples of slant and semi-slant submanifolds

Analyzed integrability conditions in Lorentzian paracosymplectic and para-Sasakian manifolds

Abstract

In this paper we define and study the slant and semi-slant submanifolds of a Lorentzian almost paracontact manifold. Some necessary and sufficient conditions for a submanifold of a Lorentzian almost paracontact manifold to be slant are obtained. We give some examples for the slant and semi-slant submanifolds of a Lorentzian almost paracontact manifold. We also investigate the integrability conditions for the distributions involved in the definition of a semi-slant submanifold when the ambient manifold is a Lorentzian paracosymplectic and a Lorentzian para-Sasakian manifold, respectively.