Existence and Nonexistence of Warped Product Submanifolds of Almost Contact Manifolds

TL;DR

This paper generalizes the conditions for the existence and nonexistence of warped product submanifolds in almost contact manifolds, providing a comprehensive reference and constructing a specific example in Kenmotsu manifolds.

Contribution

It offers a unified, general framework for understanding warped product submanifolds in almost contact manifolds and introduces a new example in Kenmotsu manifolds.

Findings

Generalized existence and nonexistence results for warped product submanifolds

Constructed a contact CR-warped product submanifold example in Kenmotsu manifold

Addressed open problems for future research

Abstract

This paper has two goals; the first is to generalize results for the existence and nonexistence of warped product submanifolds of almost contact manifolds, accordingly a self-contained reference of such submanifolds is offered to save efforts of potential research. Most of the results of this paper are general and decisive enough to generalize both discovered and not discovered results. Moreover, a discrete example of contact CR-warped product submanifold in Kenmotsu manifold is constructed. For further research direction, we addressed a couple of open problems arose from the results of this paper.