2007/07/20 by Luigi Verdiani, Wolfgang Ziller, Verdiani, Luigi +1
Mathematics · Physics and Astronomy · #53C20 #53C30 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C20 #msc:53C30
paper · pdf · doi:10.48550/arxiv.0707.3056
17 pages, 10 figures
arxiv created 2007/07/20 · openalex publication_date 2007/07/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We examine homogeneous metrics on spheres and determine which ones have positive sectional curvature. The answer is subtle and surprisingly difficult to prove. In some cases we also determine their pinching constants. This completes the classification of all homogeneous metrics with positive curvature (apart from one special Aloff Wallach space where the set of homogeneous metrics is too large).