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 |
|---|---|
| shape operator | extrinsic curvature operator via predicate surface "curvatureType" ⓘ |
| Poincaré upper half-plane model | -1 via predicate surface "hasGaussianCurvature" ⓘ |
| Poincaré upper half-plane model | -1 via predicate surface "hasSectionalCurvature" ⓘ |
| Cohen–Macaulay ring | depth via predicate surface "hasInvariant" ⓘ |
| Cohen–Macaulay ring | Krull dimension via predicate surface "hasInvariant" NERFINISHED ⓘ |
|
Clyde Arc bridge
surface form:
Clyde Arc
|
horizontal arch curvature via predicate surface "hasCurvature" ⓘ |
|
Clyde Arc bridge
surface form:
Clyde Arc
|
skewed deck alignment via predicate surface "hasCurvature" ⓘ |
| Galois extension | Galois group up to isomorphism via predicate surface "hasInvariant" ⓘ |
|
CM fields
surface form:
CM field
|
reflex field via predicate surface "hasInvariant" ⓘ |
|
CM fields
surface form:
CM field
|
CM type via predicate surface "hasInvariant" ⓘ |
|
Jacobian varieties
surface form:
Jacobian variety
|
Néron–Tate height (in arithmetic setting) via predicate surface "hasInvariant" NERFINISHED ⓘ |
| Drinfeld modules | j-invariant analogue via predicate surface "hasInvariant" ⓘ |
| Drinfeld modules | height via predicate surface "hasInvariant" ⓘ |
| Drinfeld modules | conductor via predicate surface "hasInvariant" ⓘ |
| Drinfeld modules | endomorphism ring via predicate surface "hasInvariant" ⓘ |
| S^2 × R geometry | positive via predicate surface "hasCurvatureInS2Direction" ⓘ |
| S^2 × R geometry | zero via predicate surface "hasCurvatureInRDirection" ⓘ |
| Nil geometry | non-constant sectional curvature via predicate surface "hasCurvatureProperty" ⓘ |
| Nil geometry | non-positive Ricci curvature in some directions via predicate surface "hasCurvatureProperty" ⓘ |
| Tate curve | j-invariant given by a q-expansion via predicate surface "hasInvariant" ⓘ |
| Tate curve | discriminant expressed as a q-product via predicate surface "hasInvariant" ⓘ |
| Tate curve | Tate module via predicate surface "hasInvariant" ⓘ |
| Poincaré metric | -1 via predicate surface "hasCurvature" ⓘ |
| Poincaré metric | constant negative via predicate surface "hasSectionalCurvature" ⓘ |
| Poincaré metric | -1 everywhere via predicate surface "hasSectionalCurvature" ⓘ |
|
Weierstrass points
surface form:
Weierstrass point
|
Weierstrass weight via predicate surface "hasInvariant" NERFINISHED ⓘ |
|
Weierstrass points
surface form:
Weierstrass point
|
Weierstrass semigroup via predicate surface "hasInvariant" NERFINISHED ⓘ |
| Liouville surface | energy integral of the geodesic flow via predicate surface "hasInvariant" ⓘ |
| Liouville surface | additional independent first integral in involution with the energy via predicate surface "hasInvariant" ⓘ |
| Veech surface | Veech group via predicate surface "hasInvariant" NERFINISHED ⓘ |
| Kontsevich–Zorich cocycle | Lyapunov spectrum via predicate surface "hasInvariant" ⓘ |
| Kontsevich–Zorich cocycle | Kontsevich–Zorich Lyapunov exponents via predicate surface "hasInvariant" NERFINISHED ⓘ |
|
Hurwitz surfaces
surface form:
Hurwitz surface
|
negative via predicate surface "hasCurvature" ⓘ |
| 4-sphere S^4 | 1 via predicate surface "constantSectionalCurvature" ⓘ |
|
Seifert fibered spaces
surface form:
Seifert fibered space
|
orbifold Euler characteristic of the base via predicate surface "hasInvariant" ⓘ |
|
Seifert fibered spaces
surface form:
Seifert fibered space
|
Seifert volume (in geometric cases) via predicate surface "hasInvariant" ⓘ |
| Margit Bridge | angled in the middle via predicate surface "hasCurvature" ⓘ |
|
mixed Hodge structures
surface form:
mixed Hodge structure
|
Hodge numbers of graded pieces via predicate surface "hasInvariant" ⓘ |
|
mixed Hodge structures
surface form:
mixed Hodge structure
|
weight filtration length via predicate surface "hasInvariant" ⓘ |