Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
compact differentiable manifolds
|
| gptkbp:category |
theorems in differential geometry
theorems in topology |
| gptkbp:field |
gptkb:topology
differential topology |
| gptkbp:firstPublished |
1920s
|
| gptkbp:generalizes |
gptkb:theorem_of_the_index_for_surfaces
|
| https://www.w3.org/2000/01/rdf-schema#label |
Poincaré–Hopf theorem
|
| gptkbp:namedAfter |
gptkb:Henri_Poincaré
gptkb:Heinz_Hopf |
| gptkbp:relatedTo |
gptkb:Euler_characteristic
vector fields index of a vector field |
| gptkbp:sentence |
The sum of the indices of a vector field's isolated zeros on a compact differentiable manifold equals the Euler characteristic of the manifold.
|
| gptkbp:bfsParent |
gptkb:Henri_Poincaré
|
| gptkbp:bfsLayer |
5
|