# On 4-dimensional gradient shrinking solitons

@article{Ni2007On4G, title={On 4-dimensional gradient shrinking solitons}, author={Lei Ni and Nolan Wallach}, journal={arXiv: Differential Geometry}, year={2007} }

In this paper we classify the four dimensional gradient shrinking solitons under certain curvature conditions satisfied by all solitons arising from finite time singularities of Ricci flow on compact four manifolds with positive isotropic curvature. As a corollary we generalize a result of Perelman on three dimensional gradient shrinking solitons to dimension four.

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