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2008 Classification of manifolds with weakly 1/4-pinched curvatures
Simon Brendle, Richard M. Schoen
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Acta Math. 200(1): 1-13 (2008). DOI: 10.1007/s11511-008-0022-7


We show that a compact Riemannian manifold with weakly pointwise 1/4-pinched sectional curvatures is either locally symmetric or diffeomorphic to a space form. More generally, we classify all compact, locally irreducible Riemannian manifolds M with the property that M × R2 has non-negative isotropic curvature.

Funding Statement

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.


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Simon Brendle. Richard M. Schoen. "Classification of manifolds with weakly 1/4-pinched curvatures." Acta Math. 200 (1) 1 - 13, 2008.


Received: 5 June 2007; Revised: 25 November 2007; Published: 2008
First available in Project Euclid: 31 January 2017

zbMATH: 1157.53020
MathSciNet: MR2386107
Digital Object Identifier: 10.1007/s11511-008-0022-7

Rights: 2008 © Institut Mittag-Leffler


Vol.200 • No. 1 • 2008
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