$\mathcal{P}\mathcal{R}$-anti-slant warped product submanifold of a nearly paracosymplectic manifold

TL;DR

This paper investigates the geometric properties of $\\mathcal{P}\ ext{-}\\mathcal{R}$-anti-slant warped product submanifolds within nearly paracosymplectic manifolds, establishing conditions for their integrability, geodesic foliations, and specific warped product structures.

Contribution

It introduces the concept of $\\mathcal{P}\ ext{-}\\mathcal{R}$-anti-slant warped product submanifolds, provides necessary and sufficient conditions for their properties, and offers illustrative examples.

Findings

Derived conditions for integrability of distributions.

Characterized when submanifolds are totally geodesic.

Established constraints for warped product structures.

Abstract

In this paper, we study $\mathcal{P}\mathcal{R}$-anti-slant warped product submanifold of a nearly paracosymplectic manifold $\widetilde{M}$. The necessary and sufficient condition is obtained for the distributions allied to the characterization of a $\mathcal{P}\mathcal{R}$-anti-slant submanifold being integrable and totally geodesic foliation. In addition, we have defined $\mathcal{P}\mathcal{R}$-anti-slant warped product submanifold of $\widetilde{M}$ and gave some illustrations. Finally, we extracted the constraints for a submanifold of $\widetilde{M}$ to be a $\mathcal{P}\mathcal{R}$-anti-slant warped product of the form $F\times_{f}N_{\lambda}$.