Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
complete Riemannian manifolds
|
| gptkbp:field |
gptkb:Riemannian_geometry
|
| https://www.w3.org/2000/01/rdf-schema#label |
Bonnet-Myers theorem
|
| gptkbp:implies |
compactness of manifold
finite fundamental group upper bound on diameter |
| gptkbp:namedAfter |
gptkb:Oskar_Bonnet
gptkb:Élie_Cartan gptkb:John_Milnor gptkb:Paul_Myers |
| gptkbp:publishedIn |
gptkb:Mathematische_Annalen
|
| gptkbp:relatedTo |
gptkb:Hopf-Rinow_theorem
Cheeger-Gromoll splitting theorem |
| gptkbp:sentence |
If a complete Riemannian manifold has Ricci curvature bounded below by a positive constant, then the manifold is compact and its diameter is bounded above.
|
| gptkbp:yearProved |
1935
|
| gptkbp:bfsParent |
gptkb:Riemannian_manifold
gptkb:Differential_geometry |
| gptkbp:bfsLayer |
5
|