On a classification of the gradient shrinking solitons

2007/10/16 by Ni, Lei, Wallach, Nolan · 5 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0710.3194

Abstract

The main purpose of this article is to provide an alternate proof to a result of Perelman on gradient shrinking solitons. In dimension three we also generalize the result by removing the κ-non-collapsing assumption. In high dimension this new method allows us to prove a classification result on gradient shrinking solitons with vanishing Weyl curvature tensor, which includes the rotationally symmetric ones.

Cited by

• On curvature estimates for four-dimensional gradient Ricci solitons
• Gradient Shrinking Ricci Solitons and Modified Sectional Curvature
• Gradient Shrinking Sasaki-Ricci Solitons with Harmonic Weyl Tensor
• Hamilton's identity and rigidity of complete gradient solitons
• Rigidity of Five-Dimensional shrinking gradient Ricci solitons

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