1996/09/20 by Vladimir Y. Rovenskii, Rovenskii, Vladimir Y., Victor A. Toponogov +2
Mathematics · #53C12 (Primary) 53C20 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #dg-ga #math.DG #msc:53C12 #msc:53C20
paper · pdf · doi:10.48550/arxiv.dg-ga/9609007
AMS-TeX v 2.1, 13 pages
arxiv created 1996/09/20 · openalex publication_date 1996/09/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The survey is devoted to Toponogov's conjecture, that \it if a complete simply connected Riemannian manifold with sectional curvature ≤ 4 and injectivity radius ≥ 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.