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Great sphere foliations and manifolds with curvature bounded above

Vladimir Y. Rovenskii·Victor A. Toponogov
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Abstract

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.

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Vladimir Y. Rovenskii, Victor A. Toponogov. 1996-09-20. Great sphere foliations and manifolds with curvature bounded above. https://arxiv.org/abs/dg-ga/9609007

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