Statements (15)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Hadamard_manifolds
gptkb:Riemannian_manifolds |
| gptkbp:field |
differential geometry
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cartan–Hadamard theorem
|
| gptkbp:implies |
universal covering space of a non-positively curved manifold is contractible
|
| gptkbp:namedAfter |
gptkb:Jacques_Hadamard
gptkb:Élie_Cartan |
| gptkbp:relatedTo |
gptkb:Hadamard_manifold
gptkb:Riemannian_geometry sectional curvature |
| gptkbp:sentence |
A complete, simply connected Riemannian manifold of non-positive sectional curvature is diffeomorphic to Euclidean space.
|
| gptkbp:yearProposed |
early 20th century
|
| gptkbp:bfsParent |
gptkb:Riemannian_geometry
|
| gptkbp:bfsLayer |
5
|