# On 4-dimensional gradient shrinking solitons

@article{Ni2007On4G,
author={Lei Ni and Nolan Wallach},
journal={arXiv: Differential Geometry},
year={2007}
}
• Published 16 October 2007
• Mathematics
• arXiv: Differential Geometry
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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