# Manifolds with 1/4-pinched curvature are space forms

@article{Brendle2007ManifoldsW1, title={Manifolds with 1/4-pinched curvature are space forms}, author={S. Brendle and R. Schoen}, journal={Journal of the American Mathematical Society}, year={2007}, volume={22}, pages={287-307} }

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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