On a classification of the gradient shrinking solitons

Lei Ni; Nolan Wallach

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arXiv · 0710.3194

On a classification of the gradient shrinking solitons

Lei Ni·Nolan Wallach

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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.

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BibTeX RIS

Lei Ni, Nolan Wallach. 2007-10-16. On a classification of the gradient shrinking solitons. https://arxiv.org/abs/0710.3194

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