Manifolds with 1/4-pinched Curvature are Space Forms
Differential Geometry
2008-07-18 v3 Analysis of PDEs
Abstract
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.
Keywords
Cite
@article{arxiv.0705.0766,
title = {Manifolds with 1/4-pinched Curvature are Space Forms},
author = {S. Brendle and R. M. Schoen},
journal= {arXiv preprint arXiv:0705.0766},
year = {2008}
}
Comments
Final version, to appear in J. Amer. Math. Soc