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Characterizations and integral formulae for generalized quasi-Einstein metrics

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.

preprint2012arXivOpen access
Abdênago BarrosErnani Ribeiro Jr
math.DG
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Open access2 authors1 topic
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Abdênago BarrosErnani Ribeiro Jr

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