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.

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All labels observed (6)

Label Occurrences
isConformalTo 2
inducesBijectionBetween 1
isBiholomorphism 1

Description generation (PDg)

The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.

Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning.  
# Instructions
Focus on describing the relationship, not the entities themselves. 
# Response Format
Begin the description with \' Indicates...\'
Input
Predicate: isBiholomorphismOf
Generated description
Indicates that one complex-analytic map is a biholomorphic equivalence between two complex manifolds, i.e., a holomorphic bijection whose inverse is also holomorphic.

Sample triples (7)

Subject Object
modular j-invariant SL(2,Z)\H and C via predicate surface "inducesBijectionBetween" ⓘ
T:z ↦ z+1
surface form: T : z ↦ z + 1
upper half-plane ℍ ⓘ
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 ⓘ
Möbius transformations
surface form: Möbius transformation
of the Riemann sphere via predicate surface "isBiholomorphism" ⓘ
Poincaré metric Euclidean metric via predicate surface "isConformalTo" ⓘ
Koebe function {z \in \mathbb{C} : |z| < 1} via predicate surface "isUnivalentOn" ⓘ