Manifolds with 1/4-pinched Curvature are Space Forms

Details Manifolds with 1/4-pinched Curvature are Space Forms Manifolds with 1/4-pinched Curvature are Space Forms

2007-05-06

arxiv.org/abs/0705.0766v3

Mathematics

Differential Geometry

Final version, to appear in J. Amer. Math. Soc

Scientific paper

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.

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