Geometry of pointwise pseudo-slant warped product submanifolds in a K\"ahler manifold

TL;DR

This paper investigates the geometric properties of pointwise pseudo-slant warped product submanifolds within Kähler manifolds, establishing conditions for their integrability, geodesic foliations, and characterizations as warped or Riemannian products.

Contribution

It provides necessary and sufficient conditions for such submanifolds to be warped products or Riemannian products in a Kähler manifold, advancing the understanding of their geometric structure.

Findings

Derived conditions for integrability and geodesic foliation.

Established criteria for pointwise pseudo-slant submanifolds to be warped products.

Characterized when these submanifolds are locally Riemannian products.

Abstract

The purpose of this paper is to study pointwise pseudo-slant warped product submanifolds of a K\"{a}hler manifold $\widetilde{M}$. We derive the conditions of integrability and totally geodesic foliation for the distributions allied to the characterization of a pointwise pseudo-slant submanifold of $\widetilde{M}$. The necessary and sufficient conditions for isometrically immersed pointwise pseudo-slant submanfold of $\widetilde{M}$ to be a pointwise pseudo-slant warped product and a locally Riemannian product are obtained.