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Classification of manifolds with weakly 1/4-pinched curvatures

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Acta Mathematica

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.

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Simon Brendle & Richard M. Schoen

Authors
  1. Simon Brendle
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  2. Richard M. Schoen
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Corresponding author

Correspondence to Simon Brendle.

Additional information

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.

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

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

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