Statements (14)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
complete Riemannian manifolds
|
| gptkbp:condition |
Ricci curvature bounded below by a positive constant
|
| gptkbp:field |
gptkb:Riemannian_geometry
|
| https://www.w3.org/2000/01/rdf-schema#label |
Riemannian Myers' theorem
|
| gptkbp:namedAfter |
gptkb:Sumner_Byron_Myers
|
| gptkbp:plotSummary |
manifold has diameter bounded above
manifold has finite fundamental group manifold is compact |
| gptkbp:publishedIn |
gptkb:Annals_of_Mathematics
|
| 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 |
1941
|
| gptkbp:bfsParent |
gptkb:Riemannian_geometry
|
| gptkbp:bfsLayer |
5
|