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