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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On gradient Ricci solitons with symmetry
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by Peter Petersen and William Wylie PDF
Proc. Amer. Math. Soc. 137 (2009), 2085-2092 Request permission

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
  • 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
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 2085-2092
  • MSC (2000): Primary 53C20
  • DOI: https://doi.org/10.1090/S0002-9939-09-09723-8
  • MathSciNet review: 2480290