On gradient ricci solitons with symmetry

Peter Petersen; William Wylie

doi:10.1090/S0002-9939-09-09723-8

On gradient ricci solitons with symmetry

Peter Petersen, William Wylie

Research output: Contribution to journal › Article › peer-review

104 Scopus citations

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.

Original language	English (US)
Pages (from-to)	2085-2092
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	137
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9939-09-09723-8
State	Published - Jun 2009
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-09-09723-8

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title = "On gradient ricci solitons with symmetry",

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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AB - 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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On gradient ricci solitons with symmetry

Abstract

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