Characterizations and integral formulae for generalized m-quasi-Einstein metrics
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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 . 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.
KeywordsRicci soliton quasi-Einstein metrics Bakry-Emery Ricci tensor scalar curvature
Mathematical subject classificationPrimary: 53C25, 53C20, 53C21 Secondary: 53C65
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