On rotationally invariant shrinking gradient Ricci solitons

Abstract

In this paper we study the gradient Ricci shrinking soliton equation on rotationally symmetric manifolds of dimension three and higher and prove that the only complete examples of such metrics on $S^n$, $\mathbb{R}n$ and $\mathbb{R}\times S^{n-1}$ are, respectively, the round, flat, and standard cylindrical metrics.

14 pages

Cited by in corpus (8)

• Recent Progress on Ricci Solitons
• On a classification of the gradient shrinking solitons
• On four-dimensional anti-self-dual gradient Ricci solitons
• Reduced distance based at singular time in the Ricci flow
• On gradient Ricci solitons with Symmetry
• Gradient Shrinking Solitons with Vanishing Weyl Tensor
• Rigidity of the round cylinders in Ricci shrinkers
• The Gap of the Consecutive Eigenvalues of the Drifting Laplacian on Metric Measure Spaces