- Acta Math.
- Volume 200, Number 1 (2008), 1-13.
Classification of manifolds with weakly 1/4-pinched curvatures
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.
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.
Acta Math., Volume 200, Number 1 (2008), 1-13.
Received: 5 June 2007
Revised: 25 November 2007
First available in Project Euclid: 31 January 2017
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2008 © Institut Mittag-Leffler
Brendle, Simon; Schoen, Richard M. Classification of manifolds with weakly 1/4-pinched curvatures. Acta Math. 200 (2008), no. 1, 1--13. doi:10.1007/s11511-008-0022-7. https://projecteuclid.org/euclid.acta/1485891956