INTEGRAL FORMULAE ON QUASI-EINSTEIN MANIFOLDS AND APPLICATIONS
A. BARROS, E. RIBEIRO
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Source: Crossref
Published: Dec 9, 2011
DOI: 10.1017/s0017089511000565
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Abstract The aim of this paper is to extend for the m -quasi-Einstein metrics some integral formulae obtained in [ 1 ] (C. Aquino, A. Barros and E. Ribeiro Jr., Some applications of the Hodge-de Rham decomposition to Ricci solitons, Results Math . 60 (2011), 245–254) for Ricci solitons and derive similar results achieved there. Moreover, we shall extend the m -Bakry-Emery Ricci tensor for a vector field X on a Riemannian manifold instead of a gradient field ∇ f , in order to obtain some results concerning these manifolds that generalize their correspondents to a gradient field.
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