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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
Posted:
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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- Chen, X., Lu, P. and Tian, G.: A note on uniformization of Riemann surfaces by Ricci flow. Proc. Amer. Math. Soc. 134 (2006), 3391-3393. MR 2231924 (2007d:53109)
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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
Posted:
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
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