Statements (15)
| 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 under positive Ricci curvature
finite fundamental group under positive Ricci curvature |
| gptkbp:namedAfter |
gptkb:Pierre_Ossian_Bonnet
gptkb:Sumner_Byron_Myers |
| gptkbp:publishedIn |
gptkb:Annals_of_Mathematics
|
| gptkbp:relatedTo |
gptkb:Cheeger–Gromoll_splitting_theorem
gptkb:Hopf–Rinow_theorem |
| gptkbp:sentence |
A complete Riemannian manifold with Ricci curvature bounded below by a positive constant is compact and has finite diameter.
|
| gptkbp:yearProved |
1935
|
| gptkbp:bfsParent |
gptkb:Riemannian_geometry
|
| gptkbp:bfsLayer |
5
|