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A generalization of Berger’s rigidity theorem for positively curved manifolds. (English) Zbl 0626.53032
Les AA. fournissent une classification complète des variétés Riemanniennes M de dimension \(n\geq 2\), complètes, dont la courbure sectionnelle K et le diamètre diam(M) vérifient: \[ K\geq 1\quad et\quad diam(M)=\pi /2. \] Les possibilités sont les suivantes: 1) M est une sphère-tordue (twisted sphere) et 2) M a un revêtement universel \(\tilde M\) isométrique à un espace symétrique de rang 1 (sauf peut-être si M a l’anneau de cohomologie entière de \({\mathbb{C}}aP^ 2)\). Si M est non simplement connexe l’action du groupe fondamental sur \(\tilde M\) est décrite. La bibliographie fournit des résultats connexes antérieurs.
Reviewer: R.Michel

MSC:
53C20 Global Riemannian geometry, including pinching
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References:
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