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arXiv:0705.0766 [math.DG]AbstractReferencesReviewsResources

Manifolds with 1/4-pinched Curvature are Space Forms

S. Brendle, R. M. Schoen

Published 2007-05-06, updated 2008-07-18Version 3

Let (M,g_0) be a compact Riemannian manifold with pointwise 1/4-pinched sectional curvatures. We show that the Ricci flow deforms g_0 to a constant curvature metric. The proof uses the fact, also established in this paper, that positive isotropic curvature is preserved by the Ricci flow in all dimensions. We also rely on earlier work of Hamilton and of Bohm and Wilking.

Comments: Final version, to appear in J. Amer. Math. Soc
Categories: math.DG, math.AP
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