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Classification of manifolds with weakly 1/4-pinched curvatures. (English) Zbl 1157.53020

In the present paper the authors classify up to diffeomeorphism Riemannian manifolds whose sectional curvature is weakly \(1/4\)-pinched, i.e., \(0\leq K(\pi_1)\leq 4K(\pi_2)\) for all two planes \(\pi_1, \pi_2\) in the tangent space at any point. Namely, they show that if \(M\) is a compact Riemannian manifold of dimension greater than four with weakly \(1/4\)-pinched sectional curvatures is either locally symmetric or diffeomorphic to a space form. More generally, the authors classify all compact, locally irreducible Riemannian manifolds \(M\) with the property that \(M \times \mathbb{R}^2\) has non-negative isotropic curvature.

MSC:

53C20 Global Riemannian geometry, including pinching
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