On Gradient Ricci Solitons with Symmetry
نویسندگان
چکیده
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 [12] to show that there are no noncompact cohomogeneity one shrinking gradient solitons with nonnegative curvature.
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