Quasi-Einstein manifolds with structure of warped product product

TL;DR

This paper characterizes quasi-Einstein warped product manifolds, showing under specific conditions that the fiber must be Einstein, and constructs examples of Ricci-flat Einstein warped products with non-conformally flat bases.

Contribution

It provides a classification of quasi-Einstein warped products with null Bakry-Emery tensor and constructs new Ricci-flat Einstein warped product examples.

Findings

Fiber is necessarily Einstein under certain conditions

All quasi-Einstein manifolds with null Bakry-Emery tensor are characterized

Constructed Ricci-flat Einstein warped products with non-conformally flat bases

Abstract

In this paper we prove that under certain conditions in a quasi Einstein semi Riemannian warped product the fiber is necessarily a Einstein manifold. We provide all the quasi Einstein manifolds when r Bakry Emery tensor is null, the base is conformal to an n-dimensional pseudo-Euclidean space invariant under the action of an n - 1 dimensional translation group and the fiber is Ricci flat. As an application, we have built a family of Ricci flat Einstein warped product whose base is not locally conformally flat.