bounded symmetric domain (up to biholomorphism)
C59244
concept
A bounded symmetric domain (up to biholomorphism) is a connected bounded open subset of complex Euclidean space whose biholomorphic automorphism group acts transitively and admits, at each point, an involutive automorphism reversing all geodesics through that point, considered up to biholomorphic equivalence.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Hermitian symmetric domain | 1 |
| bounded symmetric domain (up to biholomorphism) canonical | 1 |
| domain in several complex variables | 1 |
| generalization of upper half-plane | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: bounded symmetric domain (up to biholomorphism)
Generated description
A bounded symmetric domain (up to biholomorphism) is a connected bounded open subset of complex Euclidean space whose biholomorphic automorphism group acts transitively and admits, at each point, an involutive automorphism reversing all geodesics through that point, considered up to biholomorphic equivalence.
Instances (2)
| Instance | Via concept surface |
|---|---|
| Siegel upper half-space | Hermitian symmetric domain |
| Siegel domain | domain in several complex variables |