de Rham decomposition theorem
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
complete Riemannian manifolds
simply connected Riemannian manifolds |
| gptkbp:concerns |
gptkb:Riemannian_manifolds
|
| gptkbp:field |
differential geometry
|
| https://www.w3.org/2000/01/rdf-schema#label |
de Rham decomposition theorem
|
| gptkbp:implies |
unique decomposition up to order of factors
|
| gptkbp:namedAfter |
gptkb:Georges_de_Rham
|
| gptkbp:publicationYear |
1952
|
| gptkbp:publishedIn |
gptkb:Commentarii_Mathematici_Helvetici
|
| gptkbp:relatedTo |
gptkb:Euclidean_space
gptkb:Riemannian_geometry gptkb:de_Rham_cohomology isometry irreducible manifold |
| gptkbp:state |
any simply connected, complete Riemannian manifold with nonpositive sectional curvature is isometric to a product of irreducible manifolds and a Euclidean space
|
| gptkbp:bfsParent |
gptkb:Georges_de_Rham
|
| gptkbp:bfsLayer |
6
|