On gradient Ricci solitons with Symmetry

Peter Petersen; William Wylie

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arXiv · 0710.3595

On gradient Ricci solitons with Symmetry

Peter Petersen·William Wylie

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Abstract

We study gradient Ricci solitons with maximal symmetry. First we show that there are no non-trivial 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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Peter Petersen, William Wylie. 2008-09-24. On gradient Ricci solitons with Symmetry. https://arxiv.org/abs/0710.3595

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