Acta Mathematica

, Volume 200, Issue 1, pp 1-13

First online:

Classification of manifolds with weakly 1/4-pinched curvatures

  • Simon BrendleAffiliated withDepartment of Mathematics, Stanford University Email author 
  • , Richard M. SchoenAffiliated withDepartment of Mathematics, Stanford University

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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 × R 2 has non-negative isotropic curvature.