CAT(0) spaces of higher rank II

• 成果类型: Article
• 署名作者: Stadler, Stephan
• 署名单位: Max Planck Society
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01230-4
• 发表日期: 2024
• 页码: 709-743
• 关键词: local-structure; MANIFOLDS; CURVATURE; RIGIDITY

摘要

This belongs to a series of papers motivated by Ballmann's Higher Rank Rigidity Conjecture. We prove the following. Let X be a CAT(0) space with a geometric group action Gamma curved right arrow X. Suppose that every geodesic in X lies in an n-flat, n >= 2. If X contains a periodic n-flat which does not bound a flat (n + 1)-half-space, then X is a Riemannian symmetric space, a Euclidean building or non-trivially splits as a metric product. This generalizes the Higher Rank Rigidity Theorem for Hadamard manifolds with geometric group actions.