Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:citation |
Bridson, Martin R.; Haefliger, André. Metric Spaces of Non-Positive Curvature (1999)
|
| gptkbp:defines |
A geodesic metric space where geodesic triangles are at least as thin as their comparison triangles in the model space of constant curvature k.
|
| gptkbp:example |
Euclidean space is CAT(0)
hyperbolic space is CAT(-1) spherical space is CAT(1) |
| gptkbp:field |
metric geometry
|
| gptkbp:generalizes |
gptkb:CAT(0)_spaces
|
| https://www.w3.org/2000/01/rdf-schema#label |
CAT(k) spaces
|
| gptkbp:introducedIn |
1950s
|
| gptkbp:namedAfter |
gptkb:Élie_Cartan
gptkb:Karl_Friedrich_Gauss gptkb:Aleksandr_Danilovich_Aleksandrov gptkb:Victor_Andreevich_Toponogov |
| gptkbp:property |
convexity of distance function
triangle comparison property uniqueness of geodesics for CAT(0) spaces |
| gptkbp:relatedTo |
geodesic metric space
non-positive curvature |
| gptkbp:usedIn |
gptkb:topology
differential geometry geometric group theory |
| gptkbp:bfsParent |
gptkb:Aleksandrov_geometry
|
| gptkbp:bfsLayer |
6
|