, Volume 200, Issue 1, pp 1-13

Classification of manifolds with weakly 1/4-pinched curvatures

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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 × R 2 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.