isRiemannianMetricOn
P63675
predicate
Indicates that one object serves as a Riemannian metric defined on another object, typically a manifold, specifying an inner product on each tangent space.
All labels observed (4)
| Label | Occurrences |
|---|---|
| hasCanonicalRiemannianMetric | 1 |
| hasInvariantMetric | 1 |
| hasMetricTensor | 1 |
| isRiemannianMetricOn canonical | 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: isRiemannianMetricOn
Generated description
Indicates that one object serves as a Riemannian metric defined on another object, typically a manifold, specifying an inner product on each tangent space.
Sample triples (4)
| Subject | Object |
|---|---|
| Euclidean metric | Rn with standard inner product ⓘ |
| Poincaré upper half-plane model | g = (1/y²)(dx⊗dx + dy⊗dy) via predicate surface "hasMetricTensor" ⓘ |
| 4-sphere S^4 | round metric via predicate surface "hasCanonicalRiemannianMetric" ⓘ |
| Grassmann manifolds | metric induced from Killing form on Lie group via predicate surface "hasInvariantMetric" ⓘ |