Positive quaternionic Kaehler manifolds and symmetry rank

2003/08/14 by Fuquan Fang, Fang, Fuquan
Mathematics · #53C26 #57R91 #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:53C26 #msc:57R91

paper · pdf · doi:10.48550/arxiv.math/0308138

21 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

Abstract

A quaternionic Kähler manifold M is called \it positive if it has positive scalar curvature. The main purpose of this paper is to prove several connectedness theorems for quaternionic immersions in a quaternionic Kähler manifold, e.g. the Barth-Lefschetz type connectedness theorem for quaternionic submanifolds in a positive quaternionic Kähler manifold. As applications we prove that, among others, a 4m-dimensional positive quaternionic Kähler manifold with symmetry rank at least (m-2) must be either isometric to \Bbb HP^m or Gr₂(\Bbb C^m+2), if m≥ 10.

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