On the characterization of Riemannian warped product Einstein metrics

TL;DR

This paper investigates local properties of $(\

Contribution

It introduces new local characterizations of $(\

Findings

Provides local criteria for $(\

paper_type":"theoretical"}}

Abstract

We present a series of results, including local characterizations of $(\lambda,m+n)$-Einstein metrics in the context of warped product Einstein spaces. Using these local properties, we restate already known global characterizations of $(\lambda,m+n)$-Einstein manifolds from He, Petersen and Wylie.