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INTEGRAL FORMULAE ON QUASI-EINSTEIN MANIFOLDS AND APPLICATIONS

Published online by Cambridge University Press:  09 December 2011

A. BARROS  and
E. RIBEIRO JR.
A. BARROS
Affiliation:
Departamento de Matemática-Universidade Federal do Ceará, 60455-760-Fortaleza-CE, Brazil e-mail: abbarros@mat.ufc.br, ernani@mat.ufc.br
E. RIBEIRO JR.
Affiliation:
Departamento de Matemática-Universidade Federal do Ceará, 60455-760-Fortaleza-CE, Brazil e-mail: abbarros@mat.ufc.br, ernani@mat.ufc.br
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Abstract

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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.

Keywords

Primary 53C2553C2053C21secondary 53C65
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 1 , January 2012 , pp. 213 - 223
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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