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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnm152, 13 pages, doi:10.1093/imrn/rnm152 published on January 17, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

On Four-Dimensional Gradient Shrinking Solitons

Lei Ni and Nolan Wallach

Department of Mathematics, University of California at San Diego, La Jolla, CA 92093

Correspondence: Correspondence to be sent to: lni{at}math.ucsd.edu

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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