upper half-plane model of hyperbolic geometry
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
model of hyperbolic geometry
|
| gptkbp:alsoKnownAs |
gptkb:Poincaré_half-plane_model
|
| gptkbp:areaElement |
dx dy / y^2
|
| gptkbp:borders |
real axis and point at infinity
|
| gptkbp:category |
noncommutative geometry
|
| gptkbp:conformal |
yes
|
| gptkbp:describes |
gptkb:hyperbolic_plane
|
| gptkbp:dimensions |
2
|
| gptkbp:geodesics |
vertical lines
semicircles orthogonal to real axis |
| https://www.w3.org/2000/01/rdf-schema#label |
upper half-plane model of hyperbolic geometry
|
| gptkbp:introduced |
gptkb:Felix_Klein
gptkb:Henri_Poincaré |
| gptkbp:isometryGroup |
gptkb:PSL(2,_R)
|
| gptkbp:measures |
ds^2 = (dx^2 + dy^2)/y^2
|
| gptkbp:relatedTo |
gptkb:Poincaré_disk_model
|
| gptkbp:symmetry |
gptkb:PSL(2,_R)
|
| gptkbp:usedIn |
gptkb:Riemann_surfaces
complex analysis modular forms |
| gptkbp:uses |
upper half of the complex plane
|
| gptkbp:bfsParent |
gptkb:Farey_tree
|
| gptkbp:bfsLayer |
7
|