Cheeger–Gromoll splitting theorem
GPTKB entity
Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Riemannian_manifolds
|
| gptkbp:condition |
existence of a line
non-negative Ricci curvature |
| gptkbp:consequence |
manifold splits isometrically as a product
|
| gptkbp:field |
gptkb:Riemannian_geometry
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cheeger–Gromoll splitting theorem
|
| gptkbp:namedAfter |
gptkb:Detlef_Gromoll
gptkb:Jeff_Cheeger |
| gptkbp:publishedIn |
gptkb:Journal_of_Differential_Geometry
|
| gptkbp:relatedTo |
gptkb:Riemannian_manifold
Ricci curvature splitting theorem |
| gptkbp:state |
A complete, connected Riemannian manifold with non-negative Ricci curvature and containing a line is isometric to a product of the real line and another manifold.
|
| gptkbp:yearProved |
1971
|
| gptkbp:bfsParent |
gptkb:Jeff_Cheeger
|
| gptkbp:bfsLayer |
5
|