On gradient Ricci solitons with Symmetry

Details On gradient Ricci solitons with Symmetry On gradient Ricci solitons with Symmetry

2007-10-18

arxiv.org/abs/0710.3595v2

Mathematics

Differential Geometry

7 pages, final version, to appear in Proc. of AMS

Scientific paper

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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