hasCurvatureInvariant
P4461
predicate
Indicates that one entity possesses a specific curvature-related invariant property or value associated with its geometric or mathematical structure.
Observed surface forms (11)
- hasInvariant ×15
- hasCurvature ×5
- exampleConstantCurvatureSurface ×3
- hasCurvatureInvariants ×2
- curvature ×1
- hasCurvatureProperty ×1
- hasKretschmannScalar ×1
- hasRicciTensor ×1
- hasScalarCurvature ×1
- hasWeylTensor ×1
- isLocalInvariantOf ×1
Sample triples (34)
| Subject | Object |
|---|---|
|
Abelian groups
surface form:
Abelian group
|
primary decomposition for finite Abelian groups via predicate surface "hasInvariant" → |
|
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" → |
| BP Pedestrian Bridge | S-shaped plan via predicate surface "hasCurvature" → |
| Bardeen black hole model | finite everywhere via predicate surface "hasCurvatureInvariants" → |
| Echo Wall | continuous circular arc via predicate surface "hasCurvature" → |
| Euclidean space | zero via predicate surface "hasCurvature" → |
| 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" → |
| Gaussian curvature | sphere of radius R has K = 1/R^2 via predicate surface "exampleConstantCurvatureSurface" → |
| Kerr metric | Kerr parameter a = J/M via predicate surface "hasInvariant" → |
| Kerr metric | nonzero Kretschmann scalar → |
| Kähler manifold | Riemann curvature tensor has Kähler symmetries via predicate surface "hasCurvatureProperty" → |
| Lorentz group | light cone structure via predicate surface "hasInvariant" → |
| Lorentz group | spacetime interval via predicate surface "hasInvariant" → |
| Minkowski space-time | zero via predicate surface "curvature" → |
| Poincaré group | Minkowski interval via predicate surface "hasInvariant" → |
| Poincaré group | mass Casimir operator via predicate surface "hasInvariant" → |
| Poincaré group | speed of light via predicate surface "hasInvariant" → |
| Poincaré group | spin Casimir operator via predicate surface "hasInvariant" → |
| Ricci curvature tensor | metric tensor via predicate surface "isLocalInvariantOf" → |
|
Riemann surfaces
surface form:
Riemann surface
|
Euler’s polyhedron formula
via predicate surface "hasInvariant"
→
surface form:
Euler characteristic
|
|
Riemann surfaces
surface form:
Riemann surface
|
complex structure via predicate surface "hasInvariant" → |
|
Riemann surfaces
surface form:
Riemann surface
|
conformal structure via predicate surface "hasInvariant" → |
|
Riemann surfaces
surface form:
Riemann surface
|
fundamental group via predicate surface "hasInvariant" → |
|
Riemann surfaces
surface form:
Riemann surface
|
genus via predicate surface "hasInvariant" → |
| 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" → |
| de Sitter spacetime | constant via predicate surface "hasCurvatureInvariants" → |
| de Sitter spacetime | constant positive curvature via predicate surface "hasCurvature" → |
| de Sitter spacetime | constant positive value via predicate surface "hasScalarCurvature" → |
| de Sitter spacetime | proportional to metric tensor via predicate surface "hasRicciTensor" → |
| de Sitter spacetime | zero via predicate surface "hasWeylTensor" → |
| spacetime manifold | spacetime curvature via predicate surface "hasCurvature" → |