2003/08/14 by Fuquan Fang, Fang, Fuquan, Xiaochun Rong +1 · 2 citations
Mathematics · #53C20 #57R19 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #math.GT #msc:53C20 #msc:57R19
paper · pdf · doi:10.48550/arxiv.math/0308139
18 pages
arxiv created 2003/08/14 · openalex publication_date 2003/08/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a closed simply connected n-manifold of positive sectional curvature. We determine its homeomorphism or homotopic type if M also admits an isometric elementary p-group action of large rank. Our main results are: There exists a constant p(n)>0 such that (1) If M2n admits an effective isometric \Bbb Zpk-action for a prime p≥ p(n), then k≤ n and ``='' implies that M2n is homeomorphic to a sphere or a complex projective space. (2) If M2n+1 admits an isometric S1 x \Bbb Zpk-action for a prime p≥ p(n), then k≤ n and ``='' implies that M is homeomorphic to a sphere. (3) For M in (1) or (2), if n≥ 7 and k≥ [\frac3n4]+2, then M is homeomorphic to a sphere or homotopic to a complex projective space.