Characterizations and integral formulae for generalized quasi-Einstein metrics

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.

To appear on Bulletin of the Brazilian Mathematical Society (2012)

References in corpus (5)

• Recent Progress on Ricci Solitons
• On the nonexistence of quasi-Einstein metrics
• On the Bartnik extension problem for the static vacuum Einstein equations
• On the classification of warped product Einstein metrics
• Uniqueness of quasi-Einstein metrics on 3-dimensional homogeneous manifolds