Abstract
The aim of this paper is to present some structural equations for generalized m-quasi-Einstein metrics (M n, g, ∇ f, λ), which was defined recently by Catino in [11]. In addition, supposing that M n 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.
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Barros, A., Ribeiro, E. Characterizations and integral formulae for generalized m-quasi-Einstein metrics. Bull Braz Math Soc, New Series 45, 325–341 (2014). https://doi.org/10.1007/s00574-014-0051-0
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DOI: https://doi.org/10.1007/s00574-014-0051-0