Sequential warped product submanifolds having factors as holomorphic, totally real and pointwise slant

TL;DR

This paper introduces a new class of sequential warped product submanifolds in Kaehler manifolds, establishes inequalities related to their geometry, and explores conditions for equality, expanding understanding of their structure.

Contribution

It defines sequential warped product submanifolds with specific factors and derives new geometric inequalities, including Chen's inequality and a Lawson-Simons inspired pinching inequality.

Findings

Established Chen's inequality for these submanifolds.

Derived a pinching inequality inspired by Lawson and Simons.

Analyzed the equality cases and geometric implications.

Abstract

We introduce sequential warped product submanifolds of Kaehler manifolds, provide examples and establish Chen's inequality for such submanifolds. The equality case is also studied. Moreover, by inspiring Lawson and Simons's integral currrent's theorem on a submanifold, we find a similar pinching inequality for a sequential warped product submanifold and obtain geometric results when the equality case is satisfied.