Classification of Manifolds with Weakly 1/4-pinched Curvatures Simon Brendle and Richard Schoen
نویسنده
چکیده
A classical theorem due to M. Berger [2] and W. Klingenberg [11] states that a simply connected Riemannian manifold whose sectional curvatures all lie in the interval [1, 4] is either isometric to a symmetric space or homeomorphic to Sn (see also [12], Theorems 2.8.7 and 2.8.10). In this paper, we provide a classification, up to diffeomorphism, of all Riemannian manifolds whose sectional curvatures are weakly 1/4-pinched in a pointwise sense. Our main result is the following:
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