Fundamental groups of manifolds with positive sectional curvature and\n torus symmetry

2013/10/27 by Lee Kennard, Kennard, Lee · 1 citation
Mathematics · #53C20 (Primary) 55S10 #55S20 (Secondary) #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1310.7251

openalex publication_date 2013/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1965, S.-S. Chern posed a question concerning the extent to which\nfundamental groups of manifolds admitting positive sectional curvature look\nlike spherical space form groups. The original question was answered in the\nnegative by Shankar in 1998, but there are a number of positive results in the\npresence of symmetry. These classifications fall into categories according to\nthe strength of their conclusions. We give an overview of these results in the\ncase of torus symmetry and prove new results in each of these categories.\n

Citations

• Examples of Riemannian Manifolds with non-negative sectional curvature

Cited by

• Positive weighted sectional curvature

Related

• Positive curvature and discrete abelian symmetry
• Symmetries of Eschenburg spaces and the Chern problem
• Fundamental groups on manifolds with positive isotropic curvature
• Positive curvature and torus symmetry in small dimensions, I -- Dimensions 10, 12, 14, and 16
• Sectional Curvature, Isotropic Curvature, and Yau's Pinching Problem