Bounds on volume growth of geodesic balls for Einstein warped products

TL;DR

This paper derives volume estimates for Einstein warped products, extending classical results for nonnegative Ricci curvature, and identifies obstructions to their existence using quasi-Einstein manifold techniques.

Contribution

It provides new volume bounds for Einstein warped products and introduces obstructions to their existence via quasi-Einstein manifold methods.

Findings

Volume estimates for Einstein warped products

Obstructions to existence of certain Einstein warped manifolds

Connection to classical nonnegative Ricci curvature results

Abstract

The purpose of this note is to provide some volume estimates for Einstein warped products similar to a classical result due to Calabi and Yau for complete Riemannian manifolds with nonnegative Ricci curvature. To do so, we make use of the approach of quasi-Einstein manifolds which is directly related to Einstein warped product. In particular, we present an obstruction for the existence of such a class of manifolds.