On gradient Ricci solitons with Symmetry

2007/10/18 by Petersen, Peter, Wylie, William · 3 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0710.3595

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.

Cited by

• Quasi-Einstein Metrics and a curvature identity associated with the Ricci flow
• Ricci-Yamabe solitons on a Walker 3-manifold
• Expanding Ricci solitons and Higgs bundles

Related

• Cohomogeneity one 4-dimensional gradient Ricci solitons
• A rigidity theorem for codimension one shrinking gradient Ricci solitons in \mathbb Rⁿ⁺¹
• Some rigidity results on shrinking gradient Ricci soliton
• Generic Properties of Homogeneous Ricci Solitons
• On the fundamental group of steady gradient Ricci solitons with nonnegative sectional curvature