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.References
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Bibliographic Information
- Simon Brendle
- Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
- MR Author ID: 655348
- Richard Schoen
- Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
- Received by editor(s): May 7, 2007
- Published electronically: July 17, 2008
- Additional Notes: The first author was partially supported by a Sloan Foundation Fellowship and by NSF grant DMS-0605223
The second author was partially supported by NSF grant DMS-0604960. - © Copyright 2008 American Mathematical Society
- Journal: J. Amer. Math. Soc. 22 (2009), 287-307
- MSC (2000): Primary 53C20; Secondary 53C44
- DOI: https://doi.org/10.1090/S0894-0347-08-00613-9
- MathSciNet review: 2449060