Automorphism of the Riemann sphere
GPTKB entity
Statements (38)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
Automorphism |
| gptkbp:actsOn |
gptkb:Riemann_sphere
|
| gptkbp:can_be_written_as |
f(z) = (az + b)/(cz + d), ad - bc ≠ 0
|
| gptkbp:groupIsomorphicTo |
gptkb:PSL(2,_C)
gptkb:Projective_linear_group_PGL(2,_C) |
| gptkbp:groupStructure |
Group under composition
|
| gptkbp:hasApplication |
gptkb:quantum_field_theory
gptkb:string_theory gptkb:Projective_geometry Mathematical physics Complex dynamics Geometric function theory Conformal mapping Classification of Riemann surfaces |
| gptkbp:heldBy |
gptkb:Möbius_transformation
Fractional linear transformation Biholomorphic map from the Riemann sphere to itself Automorphism group of the one-point compactification of the complex plane Automorphism group of the complex projective line Automorphism group of the extended complex plane Bijective holomorphic map Conformal automorphism Holomorphic automorphism Automorphism group of the genus 0 compact Riemann surface |
| https://www.w3.org/2000/01/rdf-schema#label |
Automorphism of the Riemann sphere
|
| gptkbp:order |
Infinite
|
| gptkbp:parameter |
Four complex numbers a, b, c, d with ad - bc ≠ 0
|
| gptkbp:preserves |
Complex structure of the Riemann sphere
Conformal structure of the Riemann sphere |
| gptkbp:relatedTo |
gptkb:Complex_projective_line
gptkb:Stereographic_projection Linear fractional transformation |
| gptkbp:studiedIn |
gptkb:Algebraic_geometry
gptkb:Riemann_surface_theory Complex analysis |
| gptkbp:bfsParent |
gptkb:Linear_Fractional_Transformation
|
| gptkbp:bfsLayer |
8
|