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.
Observed surface forms (3)
- hasCanonicalRiemannianMetric ×1
- hasInvariantMetric ×1
- hasMetricTensor ×1
Sample triples (4)
| Subject | Object |
|---|---|
| 4-sphere S^4 | round metric via predicate surface "hasCanonicalRiemannianMetric" ⓘ |
| Euclidean metric | Rn with standard inner product ⓘ |
| Grassmann manifolds | metric induced from Killing form on Lie group via predicate surface "hasInvariantMetric" ⓘ |
| Poincaré upper half-plane model | g = (1/y²)(dx⊗dx + dy⊗dy) via predicate surface "hasMetricTensor" ⓘ |