Characterizations and integral formulae for generalized m-quasi-Einstein metrics

By A. Barros, E. Ribeiro. 2012

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The aim of this paper is to present some structural equations for generalized m-quasi-Einstein metrics (Mn, g, ∇ f, λ), which was defined recently by Catino in [11]. In addition, supposing that Mn is an Einstein manifold we shall show that it is a space form with a well defined potential f. Finally, we shall derive a formula for the Laplacian of its scalar curvature which will give some integral formulae for such a class of compact manifolds that permit to obtain some rigidity results.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f3c21d02f1fccda4e4828675831688129f3b1c07