Classification of manifolds with weakly 1/4-pinched curvatures
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- Brendle, S. & Schoen, R.M. Acta Math (2008) 200: 1. doi:10.1007/s11511-008-0022-7
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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.