hasCurvatureInvariant
P4461
predicate
Indicates that one entity possesses a specific curvature-related invariant property or value associated with its geometric or mathematical structure.
All labels observed (25)
| Label | Occurrences |
|---|---|
| hasInvariant | 88 |
| hasCurvature | 16 |
| curvature | 3 |
| exampleConstantCurvatureSurface | 3 |
| hasCurvatureProperty | 3 |
| hasSectionalCurvature | 3 |
| curvatureProperty | 2 |
| curvatureType | 2 |
| hasCurvatureInvariant canonical | 2 |
| hasCurvatureInvariants | 2 |
| constantSectionalCurvature | 1 |
| hasConstantScalarCurvature | 1 |
| hasCurvatureContext | 1 |
| hasCurvatureInRDirection | 1 |
| hasCurvatureInS2Direction | 1 |
| hasCurvatureType | 1 |
| hasGaussianCurvature | 1 |
| hasKretschmannScalar | 1 |
| hasRicciTensor | 1 |
| hasScalarCurvature | 1 |
| hasSectionalCurvatureSign | 1 |
| hasWeylTensor | 1 |
| isLocalInvariantOf | 1 |
| metricCurvature | 1 |
| typeOfCurvature | 1 |
Sample triples (139)
| Subject | Object |
|---|---|
| Schwarzschild black hole | Kretschmann scalar ⓘ |
|
Kretschmann scalar
surface form:
Schwarzschild metric
|
K = 48 G^2 M^2 / (c^4 r^6) via predicate surface "hasKretschmannScalar" ⓘ |
| Minkowski space-time | zero via predicate surface "curvature" ⓘ |
| Ricci curvature tensor | metric tensor via predicate surface "isLocalInvariantOf" ⓘ |
| de Sitter spacetime | constant positive curvature via predicate surface "hasCurvature" ⓘ |
| de Sitter spacetime | proportional to metric tensor via predicate surface "hasRicciTensor" ⓘ |
| de Sitter spacetime | constant positive value via predicate surface "hasScalarCurvature" ⓘ |
| de Sitter spacetime | zero via predicate surface "hasWeylTensor" ⓘ |
| de Sitter spacetime | constant via predicate surface "hasCurvatureInvariants" ⓘ |
| Kerr metric | Kerr parameter a = J/M via predicate surface "hasInvariant" ⓘ |
| Kerr metric | nonzero Kretschmann scalar ⓘ |
| BP Pedestrian Bridge | S-shaped plan via predicate surface "hasCurvature" ⓘ |
| Euclidean space | zero via predicate surface "hasCurvature" ⓘ |
| Kähler manifold | Riemann curvature tensor has Kähler symmetries via predicate surface "hasCurvatureProperty" ⓘ |
| Poincaré group | Minkowski interval via predicate surface "hasInvariant" ⓘ |
| Poincaré group | speed of light via predicate surface "hasInvariant" ⓘ |
| Poincaré group | mass Casimir operator via predicate surface "hasInvariant" ⓘ |
| Poincaré group | spin Casimir operator via predicate surface "hasInvariant" ⓘ |
| Gaussian curvature | sphere of radius R has K = 1/R^2 via predicate surface "exampleConstantCurvatureSurface" ⓘ |
| Gaussian curvature |
Euclidean space
via predicate surface "exampleConstantCurvatureSurface"
ⓘ
surface form:
Euclidean plane has K = 0
|
| Gaussian curvature | hyperbolic plane has K < 0 via predicate surface "exampleConstantCurvatureSurface" ⓘ |
| Lorentz group | spacetime interval via predicate surface "hasInvariant" ⓘ |
| Lorentz group | light cone structure via predicate surface "hasInvariant" ⓘ |
| Bardeen black hole model | finite everywhere via predicate surface "hasCurvatureInvariants" ⓘ |
|
Riemann surfaces
surface form:
Riemann surface
|
genus via predicate surface "hasInvariant" ⓘ |
|
Riemann surfaces
surface form:
Riemann surface
|
Euler’s polyhedron formula
via predicate surface "hasInvariant"
ⓘ
surface form:
Euler characteristic
|
|
Riemann surfaces
surface form:
Riemann surface
|
fundamental group via predicate surface "hasInvariant" ⓘ |
|
Riemann surfaces
surface form:
Riemann surface
|
conformal structure via predicate surface "hasInvariant" ⓘ |
|
Riemann surfaces
surface form:
Riemann surface
|
complex structure via predicate surface "hasInvariant" ⓘ |
| spacetime manifold | spacetime curvature via predicate surface "hasCurvature" ⓘ |
|
Abelian groups
surface form:
Abelian group
|
rank of an Abelian group via predicate surface "hasInvariant" ⓘ |
|
Abelian groups
surface form:
Abelian group
|
torsion subgroup via predicate surface "hasInvariant" ⓘ |
|
Abelian groups
surface form:
Abelian group
|
primary decomposition for finite Abelian groups via predicate surface "hasInvariant" ⓘ |
| Echo Wall | continuous circular arc via predicate surface "hasCurvature" ⓘ |
| Gödel metric | constant scalar curvature via predicate surface "hasCurvature" ⓘ |
| Cartan subalgebras | rank of the Lie algebra via predicate surface "hasInvariant" ⓘ |
| Calabi–Yau manifold | Hodge numbers via predicate surface "hasInvariant" ⓘ |
| Calabi–Yau manifold | Euler characteristic via predicate surface "hasInvariant" ⓘ |
| Calabi–Yau manifold | fundamental group via predicate surface "hasInvariant" ⓘ |
| Calabi–Yau manifold | Picard number via predicate surface "hasInvariant" ⓘ |
| Calabi–Yau manifold | Kähler cone via predicate surface "hasInvariant" ⓘ |
| Calabi–Yau manifold | complex structure moduli via predicate surface "hasInvariant" ⓘ |
| Calabi–Yau manifold | Kähler moduli via predicate surface "hasInvariant" ⓘ |
| anti-de Sitter space | constant negative curvature via predicate surface "hasCurvature" ⓘ |
| anti-de Sitter space | negative via predicate surface "hasSectionalCurvatureSign" ⓘ |
| anti-de Sitter space | true via predicate surface "hasConstantScalarCurvature" ⓘ |
| anti-de Sitter space | constant negative sectional curvature via predicate surface "hasCurvatureType" ⓘ |
| Grey Street | sweeping curve via predicate surface "hasCurvature" ⓘ |
| Gauss’s remarkable theorem | sectional curvature in dimension two via predicate surface "typeOfCurvature" ⓘ |
|
cyclotomic fields
surface form:
cyclotomic field
|
Euler totient φ(n) as its degree over Q via predicate surface "hasInvariant" ⓘ |