Biwarped product submanifolds of a K\"{a}hler manifold

TL;DR

This paper investigates biwarped product submanifolds within Kähler manifolds, establishing existence conditions, inequalities involving the second fundamental form, and criteria for local triviality, with illustrative examples and theoretical analysis.

Contribution

It introduces new conditions and inequalities for biwarped product submanifolds in Kähler manifolds, including existence criteria and the characterization of trivial cases.

Findings

Non-existence of certain biwarped product submanifolds under specific conditions

Existence of non-trivial examples demonstrating the concepts

An inequality relating the second fundamental form and warping functions

Abstract

We study biwarped product submanifolds which are special cases of multiply warped product submanifolds in K\"{a}hler manifolds. We observe the non-existence of such submanifolds under some circumstances. We show that there exists a non-trivial biwarped product submanifold of a certain type by giving an illustrate example. We also give a necessary and sufficient condition for such submanifolds to be locally trivial. Moreover, we establish an inequality for the squared norm of the second fundamental form in terms of the warping functions for such submanifolds. The equality case is also discussed.