Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
gptkb:quantum_field_theory
gptkb:topology gptkb:string_theory dynamical systems integrable systems mathematical physics modular forms number theory potential theory |
| gptkbp:class |
by compactness
by conformal equivalence by genus by orientability |
| gptkbp:defines |
one-dimensional complex manifolds
|
| gptkbp:dimensions |
one complex dimension
two real dimensions |
| gptkbp:example |
gptkb:complex_plane
gptkb:butter gptkb:Riemann_sphere hyperelliptic curve |
| gptkbp:field |
gptkb:algebraic_geometry
complex analysis differential geometry |
| https://www.w3.org/2000/01/rdf-schema#label |
Riemann surfaces
|
| gptkbp:namedAfter |
gptkb:Bernhard_Riemann
|
| gptkbp:property |
can be compact or non-compact
every compact Riemann surface is an algebraic curve admit holomorphic charts can be classified by genus can be orientable transition maps are holomorphic locally homeomorphic to open subsets of the complex plane |
| gptkbp:relatedTo |
gptkb:fundamental_group
gptkb:Teichmüller_space gptkb:universal_covering_surface moduli space holomorphic functions algebraic curves automorphism group meromorphic functions covering spaces |
| gptkbp:studiedBy |
gptkb:Felix_Klein
gptkb:Henri_Poincaré gptkb:Oswald_Teichmüller gptkb:Bernhard_Riemann |
| gptkbp:usedFor |
studying analytic continuation
studying conformal mappings studying multi-valued functions |
| gptkbp:bfsParent |
gptkb:modular_group
|
| gptkbp:bfsLayer |
5
|