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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some characterizations for compact almost Ricci solitons


Authors: A. Barros and E. Ribeiro Jr.
Journal: Proc. Amer. Math. Soc. 140 (2012), 1033-1040
MSC (2010): Primary 53C25, 53C20, 53C21; Secondary 53C65
Published electronically: July 22, 2011
MathSciNet review: 2869087
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Abstract: The aim of this paper is to find some equations of structure for almost Ricci solitons which generalize the equivalent for Ricci solitons. As a consequence of these equations we derive an integral formula for the compact case which enables us to show that a compact nontrivial almost Ricci soliton is isometric to a sphere provided either it has constant scalar curvature or its associated vector field is conformal. Moreover, we also use the Hodge-de Rham decomposition theorem to make a link with the associated vector field of an almost Ricci soliton.


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Additional Information

A. Barros
Affiliation: Departamento de Matemática, Universidade Federal do Ceara, 60455-760, Fortaleza-CE, Brazil
Email: abbarros@mat.ufc.br

E. Ribeiro Jr.
Affiliation: Departamento de Matemática, Universidade Federal do Ceara, 60455-760, Fortaleza-CE, Brazil
Email: ernani@mat.ufc.br

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11029-3
PII: S 0002-9939(2011)11029-3
Keywords: Ricci soliton, almost Ricci soliton, Hodge-de Rham, scalar curvature
Received by editor(s): October 19, 2010
Received by editor(s) in revised form: December 20, 2010
Published electronically: July 22, 2011
Additional Notes: The first author was partially supported by CNPq-BR
The second author was partially supported by CAPES-BR
Communicated by: Jianguo Cao
Article copyright: © Copyright 2011 American Mathematical Society