Warped Product Pointwise Semi-slant Submanifolds of Almost Contact Manifolds

TL;DR

This paper explores the geometry of warped product pointwise semi-slant submanifolds within almost contact manifolds, establishing existence conditions and providing examples and characterizations.

Contribution

It introduces the concept of warped product pointwise semi-slant submanifolds in almost contact manifolds and characterizes their properties, including non-existence results and examples.

Findings

No proper pointwise semi-slant warped product submanifolds exist other than contact CR-warped products in Sasakian manifolds.

Constructed non-trivial examples in cosymplectic manifolds.

Provided fundamental characterizations of these submanifolds.

Abstract

Recently, B.-Y. Chen and O. J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. By using the notion of pointwise slant submanifolds, we investigate the geometry of pointwise semi-slant submanifolds and their warped products in Sasakian and cosymplectic manifolds. We prove that there exist no proper pointwise semi-slant warped product submanifold other than contact CR-warped products in Sasakian manifolds. We give non-trivial examples of such submanifolds in cosypmlectic manifolds and obtain several fundamental results, including a characterization for warped product pointwise semi-slant submanifolds.