On the estimates of warping functions on isometric immersions

TL;DR

This paper derives estimates for warping functions in isometric immersions into various Riemannian manifolds, explores equality cases, and discusses applications and open problems in the field.

Contribution

It extends previous results by providing new estimates of warping functions for immersions into constant space forms and Hermitian symmetric spaces, including analysis of equality cases.

Findings

Derived new estimates for warping functions in specific target manifolds.

Analyzed conditions for equality cases in these estimates.

Presented applications and posed open problems for future research.

Abstract

Using the results of \cite{P1}, we get some estimates of warping functions for isometric immersions by changing the target manifolds by some types of Riemannian manifolds: constant space forms and Hermitian symmetric spaces. And we deal with equality cases and obtain their applications. Finally, we give some open problems.