isBiholomorphismOf
P160143
predicate
Indicates that one complex-analytic map is a biholomorphic equivalence between two complex manifolds, i.e., a holomorphic bijection whose inverse is also holomorphic.
Observed surface forms (5)
- isConformalTo ×2
- inducesBijectionBetween ×1
- isBiholomorphism ×1
- isConformallyEquivalentTo ×1
- isUnivalentOn ×1
Sample triples (7)
| Subject | Object |
|---|---|
| Koebe function | {z \in \mathbb{C} : |z| < 1} via predicate surface "isUnivalentOn" ⓘ |
|
Möbius transformations
surface form:
Möbius transformation
|
of the Riemann sphere via predicate surface "isBiholomorphism" ⓘ |
| Poincaré metric | Euclidean metric via predicate surface "isConformalTo" ⓘ |
| Poincaré upper half-plane model | Euclidean upper half-plane via predicate surface "isConformalTo" NERFINISHED ⓘ |
| Poincaré upper half-plane model | Poincaré disk model via predicate surface "isConformallyEquivalentTo" NERFINISHED ⓘ |
|
T:z ↦ z+1
surface form:
T : z ↦ z + 1
|
upper half-plane ℍ ⓘ |
| modular j-invariant | SL(2,Z)\H and C via predicate surface "inducesBijectionBetween" ⓘ |