Classification of manifolds with weakly 1/4-pinched curvatures

Simon Brendle, Richard Schoen

Type: Article

Publication Date: 2008-01-01

Citations: 114

DOI: https://doi.org/10.1007/s11511-008-0022-7

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.

Locations

Acta Mathematica - View - PDF
arXiv (Cornell University) - View - PDF

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