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- Title
On splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature.
- Authors
Hosaka, Tetsuya
- Abstract
In this paper, we show some splitting theorems for CAT(0) spaces on which a product group acts geometrically and we obtain a splitting theorem for compact geodesic spaces of non-positive curvature. A CAT(0) group Γ is said to be rigid, if Γ determines its boundary up to homeomorphisms of a CAT(0) space on which Γ acts geometrically. C. Croke and B. Kleiner have constructed a non-rigid CAT(0) group. As an application of the splitting theorems for CAT(0) spaces, we obtain that if Γ and Γ are rigid CAT(0) groups then so is Γ × Γ.
- Subjects
CURVATURE; GEODESIC spaces; DIFFERENTIAL geometry; HOMEOMORPHISMS; MANIFOLDS (Mathematics)
- Publication
Mathematische Zeitschrift, 2012, Vol 272, Issue 3/4, p1037
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-011-0972-x