Great sphere foliations and manifolds with curvature bounded above

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The survey is devoted to Toponogov's conjecture, that {\it if a complete simply connected Riemannian manifold with sectional curvature $\le 4$ and injectivity radius $\ge π/2$ has extremal diameter $π/2$, then it is isometric to CROSS}. In Section 1 the relations of problem with geodesic foliations of a round sphere are considered, but the proof of conjecture on this way is not complete. In Section 2 the proof based on recent results and methods for topology and volume of Blaschke manifolds is given.
AMS-TeX v 2.1, 13 pages

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Differential Geometry, 53C12 (Primary) 53C20 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/152165

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/dg-ga/9609007
 http://arxiv.org/abs/dg-ga/9609007

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arXiv