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Differentiable structure of spheres and curvature. (English) Zbl 0788.53026

Greene, Robert (ed.) et al., Differential geometry. Part 3: Riemannian geometry. Proceedings of a summer research institute, held at the University of California, Los Angeles, CA, USA, July 8-28, 1990. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 54, Part 3, 609-614 (1993).
Summary: Let \((M,g)\) be a complete, simply connected Riemannian manifold of dimension \(n\). The purposes of this note are to present a new pinching constant in the differentiable pinching problem, and to indicate the idea of its proof in comparison with related results. A detailed account will be published elsewhere [the author, J. Math. Soc. Japan 43, No. 3, 527- 553 (1991)].
For the entire collection see [Zbl 0773.00024].

MSC:

53C20 Global Riemannian geometry, including pinching
53C22 Geodesics in global differential geometry
58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
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