Disambiguation evidence for Riemann surfaces via surface form
"Riemann surface"
As subject (58)
Triples where this entity appears as subject under the
label "Riemann surface".
| Predicate | Object |
|---|---|
| admits | conformal metric ⓘ |
| admits | holomorphic 1-forms ⓘ |
| admits | holomorphic functions ⓘ |
| admits | meromorphic functions ⓘ |
| classifiedBy | genus in the compact case ⓘ |
| compactCaseCorrespondsTo | smooth projective algebraic curves over the complex numbers ⓘ |
| definedOver | complex numbers ⓘ |
| dimension | one complex dimension ⓘ |
| equivalentTo | one-dimensional complex analytic manifold ⓘ |
| equivalentTo | one-dimensional complex manifold with holomorphic transition maps ⓘ |
| example | Riemann sphere ⓘ |
| example | compact Riemann surface of genus g ⓘ |
| example | complex plane ⓘ |
| example | complex torus ⓘ |
| example | unit disk with its complex structure ⓘ |
| field | algebraic geometry ⓘ |
| field | complex analysis ⓘ |
| field | differential geometry ⓘ |
| field | topology ⓘ |
| generalizes | branched coverings of the complex plane ⓘ |
| generalizes | open subsets of the complex plane ⓘ |
| hasInvariant |
Euler’s polyhedron formula
ⓘ
surface form:
Euler characteristic
|
| hasInvariant | complex structure ⓘ |
| hasInvariant | conformal structure ⓘ |
| hasInvariant | fundamental group ⓘ |
| hasInvariant | genus ⓘ |
| hasProperty | Hausdorff ⓘ |
| hasProperty | connected (usually assumed in the definition) ⓘ |
| hasProperty | orientable ⓘ |
| hasProperty | second countable ⓘ |
| hasTheorem | Hodge decomposition for compact Riemann surfaces ⓘ |
| hasTheorem | Riemann–Hurwitz formula ⓘ |
| hasTheorem | Riemann–Roch theorem ⓘ |
| hasTheorem | uniformization theorem ⓘ |
| instanceOf | analytic space ⓘ |
| instanceOf | complex manifold ⓘ |
| instanceOf | mathematical concept ⓘ |
| instanceOf | one-dimensional complex manifold ⓘ |
| instanceOf | topological space ⓘ |
| localModel | open subsets of the complex plane ⓘ |
| namedAfter | Bernhard Riemann ⓘ |
| orientationInducedBy | complex structure ⓘ |
| realDimension | two real dimensions ⓘ |
| relatedTo | Fuchsian group ⓘ |
| relatedTo | Kleinian group ⓘ |
| relatedTo | algebraic curve ⓘ |
| relatedTo | complex curve ⓘ |
| relatedTo | moduli space of curves ⓘ |
| structure | atlas of charts to the complex plane ⓘ |
| transitionMaps | holomorphic functions ⓘ |
| usedFor | Teichmüller theory ⓘ |
| usedFor | analytic continuation ⓘ |
| usedFor | moduli problems in algebraic geometry ⓘ |
| usedFor | monodromy theory ⓘ |
| usedFor | studying complex analytic functions ⓘ |
| usedFor | studying multi-valued analytic functions ⓘ |
| usedFor | theory of algebraic curves ⓘ |
| usedFor | uniformization theory ⓘ |