curvatureCondition
P161401
predicate
Indicates that a specified geometric object or path satisfies a particular constraint or requirement on its curvature.
All labels observed (3)
| Label | Occurrences |
|---|---|
| curvatureCondition canonical | 2 |
| hasCurvatureCondition | 1 |
| sectionalCurvatureInPlanesContainingRDirection | 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: curvatureCondition
Generated description
Indicates that a specified geometric object or path satisfies a particular constraint or requirement on its curvature.
Sample triples (4)
| Subject | Object |
|---|---|
| Hopf conjecture (on Euler characteristic and curvature) | everywhere positive sectional curvature ⓘ |
| Hopf conjecture (on Euler characteristic and curvature) | everywhere negative sectional curvature ⓘ |
| Three-manifolds with positive Ricci curvature | positive Ricci curvature via predicate surface "hasCurvatureCondition" ⓘ |
| S^2 × R geometry | nonpositive or zero depending on metric choice via predicate surface "sectionalCurvatureInPlanesContainingRDirection" ⓘ |