Disambiguation evidence for Riemannian manifolds via surface form
"Riemannian manifold"
As subject (47)
Triples where this entity appears as subject under the
label "Riemannian manifold".
| Predicate | Object |
|---|---|
| allows | definition of curvature ⓘ |
| allows | definition of geodesics ⓘ |
| allows | measurement of angles between tangent vectors ⓘ |
| allows | measurement of areas and volumes ⓘ |
| allows | measurement of lengths of curves ⓘ |
| contrastsWith | Finsler manifold ⓘ |
| contrastsWith | pseudo-Riemannian manifold ⓘ |
| definedAs | smooth manifold equipped with an inner product on each tangent space ⓘ |
| enables | definition of distance function ⓘ |
| enables | definition of divergence and Laplace–Beltrami operator ⓘ |
| enables | definition of gradient of functions ⓘ |
| enables | integration of scalar fields and differential forms ⓘ |
| field |
Riemannian manifolds
self-linksurface differs
ⓘ
surface form:
Riemannian geometry
|
| field | differential geometry ⓘ |
| generalizes | Euclidean space ⓘ |
| generalizes | curved surfaces ⓘ |
| hasComponent | Levi-Civita connection ⓘ |
| hasComponent | Riemann curvature tensor ⓘ |
| hasComponent | metric tensor ⓘ |
| hasComponent | tangent bundle ⓘ |
| hasDimension | any positive integer ⓘ |
| hasHistoricalOrigin | 19th century ⓘ |
| hasPart | Riemannian metric ⓘ |
| hasPart | smooth manifold ⓘ |
| hasProperty | locally Euclidean as a topological space ⓘ |
| hasProperty | positive-definite metric tensor ⓘ |
| hasProperty | smooth structure ⓘ |
| hasVariant | Einstein manifold ⓘ |
| hasVariant | Kähler manifold ⓘ |
| hasVariant |
Riemannian manifolds
self-linksurface differs
ⓘ
surface form:
Riemannian surface
|
| hasVariant | compact Riemannian manifold ⓘ |
| hasVariant | complete Riemannian manifold ⓘ |
| instanceOf | differential geometric object ⓘ |
| instanceOf | geometric structure ⓘ |
| instanceOf | mathematical object ⓘ |
| introducedBy | Bernhard Riemann ⓘ |
| namedAfter | Bernhard Riemann ⓘ |
| requires | smoothness of metric tensor ⓘ |
| requires | smoothness of transition maps ⓘ |
| specialCaseOf | smooth manifold with additional structure ⓘ |
| studiedIn | comparison geometry ⓘ |
| studiedIn | global Riemannian geometry ⓘ |
| studiedIn | spectral geometry ⓘ |
| usedIn |
theory of relativity
ⓘ
surface form:
general relativity
|
| usedIn | geometric analysis ⓘ |
| usedIn | global analysis ⓘ |
| usedIn | topology via metric methods ⓘ |
As object (3)
Triples where some other subject referred to this entity
as "Riemannian manifold".
Über die Hypothesen, welche der Geometrie zu Grunde liegen
→
introduces
→
"Riemannian manifold"
ⓘ
↳ resolves to Riemannian manifolds
surface form:
Friedrich Bernhard Riemann