Statements (74)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Architect
|
| gptkbp:canBe |
complex plane
|
| gptkbp:canSupport |
analytic functions
holomorphic functions meromorphic functions differential forms Riemannian metrics Riemann surfaces of different genera conformal structures |
| gptkbp:field |
one
|
| https://www.w3.org/2000/01/rdf-schema#label |
Riemann surface
|
| gptkbp:isA |
topological space
complex structure Riemannian manifold complex manifold geometric object algebraic topology object analytic space complex algebraic variety complex analytic space complex manifold with boundary complex projective variety differential geometry object two-dimensional manifold |
| gptkbp:isAccessibleBy |
complex functions
local charts local homeomorphisms |
| gptkbp:isCharacterizedBy |
genus
|
| gptkbp:isConnectedTo |
moduli space
|
| gptkbp:isCounteredBy |
algebraic topology
charts analytic continuation complex coordinates |
| gptkbp:isNamedAfter |
gptkb:Bernhard_Riemann
|
| gptkbp:isRelatedTo |
algebraic curves
modular forms sheaf theory topological invariants differential equations complex geometry complex manifolds Cauchy-Riemann equations complex function theory Riemann surfaces of higher genus complex analysis techniques Riemann-Roch_theorem |
| gptkbp:isStudiedIn |
geometry
mathematical physics |
| gptkbp:isUsedFor |
topological properties
higher-dimensional spaces coordinate charts |
| gptkbp:isUsedIn |
cryptography
string theory theoretical physics mathematical modeling number theory mathematical analysis mathematical research theory of functions complex analysis dynamical systems theory of relativity mathematical physics applications quantum_field_theory |
| gptkbp:mayHave |
homology theory
singularities topological methods sheaf cohomology non-trivial topology automorphisms branch points multiple sheets branch cuts finite covers |