Mathematics > Differential Geometry
[Submitted on 16 Oct 2007]
Title:On a classification of the gradient shrinking solitons
View PDFAbstract: 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 $\kappa$-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.
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