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

 

On gradient Ricci solitons with symmetry


Authors: Peter Petersen and William Wylie
Journal: Proc. Amer. Math. Soc. 137 (2009), 2085-2092
MSC (2000): Primary 53C20
Published electronically: January 22, 2009
MathSciNet review: 2480290
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Abstract: We study gradient Ricci solitons with maximal symmetry. First we show that there are no nontrivial homogeneous gradient Ricci solitons. Thus, the most symmetry one can expect is an isometric cohomogeneity one group action. Many examples of cohomogeneity one gradient solitons have been constructed. However, we apply the main result in our paper ``Rigidity of gradient Ricci solitons'' to show that there are no noncompact cohomogeneity one shrinking gradient solitons with nonnegative curvature.


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Additional Information

Peter Petersen
Affiliation: Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, California 90095
Email: petersen@math.ucla.edu

William Wylie
Affiliation: Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, California 90095
Address at time of publication: Department of Mathematics, David Rittenhouse Laboratory, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104-6395
Email: wylie@math.upenn.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09723-8
PII: S 0002-9939(09)09723-8
Received by editor(s): October 12, 2007
Received by editor(s) in revised form: August 5, 2008
Published electronically: January 22, 2009
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.