An almost splitting theorem for a warped product space

TL;DR

This paper establishes an almost splitting theorem for a specific class of warped product spaces characterized by a hyperbolic cosine warping function, advancing understanding of their geometric structure.

Contribution

It introduces an almost splitting theorem tailored for warped product spaces with a hyperbolic cosine warping function, extending geometric analysis in this context.

Findings

Proves an almost splitting theorem for the specified warped product space.

Identifies conditions under which the space nearly splits into simpler components.

Provides insights into the geometric structure influenced by the warping function.

Abstract

We prove an almost splitting theorem for the warped product space with warped function $f(r)=\cosh\left(r\sqrt{\frac{\lambda}{n-2}}\right)$.