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 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: hasCurvatureInvariant
Generated description
Indicates that one entity possesses a specific curvature-related invariant property or value associated with its geometric or mathematical structure.
Sample triples (139)
| Subject | Object |
|---|---|
| Onsager algebra | Casimir-like elements in certain representations via predicate surface "hasInvariant" ⓘ |
| Farey tessellation | constant negative curvature via predicate surface "hasCurvatureContext" ⓘ |
| Selberg class | degree of an L-function via predicate surface "hasInvariant" ⓘ |
| Selberg class | conductor of an L-function via predicate surface "hasInvariant" ⓘ |
| K-theory | K0 group via predicate surface "hasInvariant" ⓘ |
| K-theory | K1 group via predicate surface "hasInvariant" ⓘ |
| K-theory | higher K-groups via predicate surface "hasInvariant" ⓘ |
| Kleinian group | limit set Hausdorff dimension via predicate surface "hasInvariant" ⓘ |
| Kleinian group | critical exponent of Poincaré series via predicate surface "hasInvariant" ⓘ |
| Kleinian group | conformal dimension of limit set via predicate surface "hasInvariant" ⓘ |
| Kleinian group | volume of associated hyperbolic 3-manifold via predicate surface "hasInvariant" ⓘ |
| Riemann sphere | constant positive curvature in standard metric via predicate surface "curvature" ⓘ |
|
Dedekind zeta functions
surface form:
Dedekind zeta function
|
residue at s = 1 via predicate surface "hasInvariant" ⓘ |
| Hurwitz space | dimension determined by Riemann–Hurwitz formula via predicate surface "hasInvariant" ⓘ |
|
L-functions
surface form:
L-function
|
conductor via predicate surface "hasInvariant" ⓘ |
|
L-functions
surface form:
L-function
|
gamma factor via predicate surface "hasInvariant" ⓘ |
|
L-functions
surface form:
L-function
|
root number via predicate surface "hasInvariant" ⓘ |
|
L-functions
surface form:
L-function
|
degree via predicate surface "hasInvariant" ⓘ |
| Nordström's scalar theory of gravitation | zero via predicate surface "metricCurvature" ⓘ |
| Minkowski metric η_{μν} | zero via predicate surface "curvature" ⓘ |
|
Victoria Street
surface form:
Victoria Street (Edinburgh)
|
curved via predicate surface "hasCurvature" ⓘ |
| Fredholm operator | index(T) = dim ker(T) − codim ran(T) via predicate surface "hasInvariant" ⓘ |
| Fredholm operator | stable index under compact perturbations via predicate surface "hasInvariant" ⓘ |
| Fredholm operator | index(T*) = − index(T) via predicate surface "hasInvariant" ⓘ |
| Einstein static universe | positive spatial curvature via predicate surface "hasCurvature" ⓘ |
| affine Lie algebras | Cartan matrix of affine type via predicate surface "hasInvariant" ⓘ |
| affine Lie algebras | affine Weyl group via predicate surface "hasInvariant" NERFINISHED ⓘ |
| affine Lie algebras | level of a representation via predicate surface "hasInvariant" ⓘ |
| affine Lie algebras | central charge in associated conformal field theory via predicate surface "hasInvariant" ⓘ |
| Waring's problem | g(k) via predicate surface "hasInvariant" ⓘ |
| Waring's problem | G(k) via predicate surface "hasInvariant" ⓘ |
| Hoare partition scheme | elements left of left index are ≤ pivot candidate region via predicate surface "hasInvariant" ⓘ |
| Hoare partition scheme | elements right of right index are ≥ pivot candidate region via predicate surface "hasInvariant" ⓘ |
| Fuchsian differential equation | monodromy representation via predicate surface "hasInvariant" ⓘ |
| Fuchsian differential equation | local exponents at singular points via predicate surface "hasInvariant" ⓘ |
| Fuchsian group | limit set on the boundary of the hyperbolic plane via predicate surface "hasInvariant" ⓘ |
| Fuchsian group | Hausdorff dimension of limit set via predicate surface "hasInvariant" ⓘ |
| Fuchsian group | covolume in PSL(2,R) via predicate surface "hasInvariant" ⓘ |
| Weyl geometry | Weyl curvature via predicate surface "hasInvariant" ⓘ |
| Weyl geometry | conformal curvature via predicate surface "hasInvariant" ⓘ |
| Bergman metric | has negative holomorphic sectional curvature on the unit ball via predicate surface "curvatureProperty" ⓘ |
| Bergman metric | has constant holomorphic sectional curvature on the unit ball via predicate surface "curvatureProperty" ⓘ |
| Ehresmann connection | Ehresmann curvature via predicate surface "hasCurvature" NERFINISHED ⓘ |
| Möbius geometry | cross-ratio of four points via predicate surface "hasInvariant" ⓘ |
| Möbius geometry | angles between curves via predicate surface "hasInvariant" ⓘ |
| Hirzebruch signature theorem | Hirzebruch L-polynomial via predicate surface "hasInvariant" NERFINISHED ⓘ |
|
Nirenberg problem in differential geometry
surface form:
Nirenberg problem
|
Gaussian curvature via predicate surface "curvatureType" ⓘ |
| Dedekind domain | ideal class group via predicate surface "hasInvariant" ⓘ |
| Dedekind domain | unit group via predicate surface "hasInvariant" ⓘ |
| Dedekind domain | discriminant of its field of fractions (in number field case) via predicate surface "hasInvariant" ⓘ |