Manifolds with 1/4-pinched curvature are space forms

Brendle, Simon; Schoen, Richard

doi:10.1090/S0894-0347-08-00613-9

Manifolds with $1/4$-pinched curvature are space forms
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by Simon Brendle and Richard Schoen

J. Amer. Math. Soc. 22 (2009), 287-307

DOI: https://doi.org/10.1090/S0894-0347-08-00613-9

Published electronically: July 17, 2008

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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 Böhm and Wilking.

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