Quasi-Einstein manifolds with structure of warped product product

2019/05/02 by Bonfim, Paula Gonçalves Correia, Pina, Romildo
#53C21 53C50 53C25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.02006

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.

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