Geometry of warped product semi-slant submanifolds of Kenmotsu manifolds

TL;DR

This paper investigates the geometry of semi-slant submanifolds and their warped products within Kenmotsu manifolds, providing existence conditions, bounds on curvature, and applications.

Contribution

It introduces new characterizations and bounds for warped product semi-slant submanifolds in Kenmotsu manifolds, including an example and equality conditions.

Findings

Existence of warped product semi-slant submanifolds demonstrated by example

A lower bound for the squared norm of the second fundamental form established

Conditions for equality case analyzed and applications provided

Abstract

In this paper, we study semi-slant submanifolds and their warped products in Kenmotsu manifolds. The existence of such warped products in Kenmotsu manifolds is shown by an example and a characterization. A sharp relation is obtained as a lower bound of the squared norm of second fundamental form in terms of the warping function and the slant angle. The equality case is also considered in this paper. Finally, we provide some applications of our derived results.