Warped Product Pointwise Semi-slant Submanifolds of Kaehler Manifolds

TL;DR

This paper introduces and constructs non-trivial warped product pointwise semi-slant submanifolds in Kaehler manifolds, providing characterizations, inequalities, and examples that contrast with known results for semi-slant submanifolds.

Contribution

It is the first to demonstrate the existence of warped product pointwise semi-slant submanifolds in Kaehler manifolds and establishes related geometric inequalities.

Findings

Existence of non-trivial warped product pointwise semi-slant submanifolds.

A characterization theorem for these submanifolds.

An inequality involving the second fundamental form and warping function.

Abstract

It is known that there exist no warped product semi-slant submanifolds in Kaehler manifolds \cite{Sahin}. Recently, Chen and Garay studied pointwise-slant submanifolds of almost Hermitian manifolds in \cite{CG} and obtained many new results for such submanifolds. In this paper, we first introduce pointwise semi-slant submanifolds of Kaehler manifolds and then we show that there exists non-trivial warped product pointwise semi-slant submanifolds of Kaehler manifold by giving an example, contrary to the semi-slant case. We present a characterization theorem and establish an inequality for the squared norm of the second fundamental form in terms of the warping function for such warped product submanifolds in Kaehler manifolds. The equality case is also considered.