Characterizations and integral formulae for generalized quasi-Einstein metrics
Differential Geometry
2012-09-13 v2
Abstract
The aim of this paper is to present some structural equations for generalized quasi-Einstein metrics which was defined recently by Catino in [12]. In addition, supposing that the Riemannian manifold is Einstein we shall show that it is a space form with a well defined potential function f. Finally, we shall derive some integral formulae for such a class of compact manifolds which permit to obtain some rigidity results.
Cite
@article{arxiv.1206.4980,
title = {Characterizations and integral formulae for generalized quasi-Einstein metrics},
author = {Abdênago Barros and Ernani Ribeiro},
journal= {arXiv preprint arXiv:1206.4980},
year = {2012}
}
Comments
To appear on Bulletin of the Brazilian Mathematical Society (2012)