Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:citation |
Bridson, Martin R.; Haefliger, André (1999), Metric Spaces of Non-Positive Curvature
|
| gptkbp:defines |
A geodesic metric space in which geodesic triangles are at least as thin as their comparison triangles in Euclidean space
|
| gptkbp:example |
gptkb:Euclidean_space
gptkb:Hilbert_space gptkb:Hadamard_manifold trees (in graph theory) |
| gptkbp:field |
geometric group theory
metric geometry |
| gptkbp:hasProperty |
fixed point property for group actions by isometries
unique geodesics between points convex metric balls |
| https://www.w3.org/2000/01/rdf-schema#label |
CAT(0) space
|
| gptkbp:introducedIn |
1950s
|
| gptkbp:namedAfter |
gptkb:Élie_Cartan
gptkb:Alexandrov gptkb:Toponogov |
| gptkbp:property |
contractible
non-positive curvature in the sense of Alexandrov uniquely geodesic |
| gptkbp:relatedTo |
gptkb:CAT(k)_space
gptkb:Riemannian_manifold Gromov hyperbolic space |
| gptkbp:usedIn |
gptkb:topology
geometric group theory group actions |
| gptkbp:bfsParent |
gptkb:CAT(0)_groups
gptkb:CAT(k)_space |
| gptkbp:bfsLayer |
7
|