Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
A smooth map between Riemannian manifolds that is a submersion and preserves the length of horizontal vectors.
|
| gptkbp:example |
gptkb:Hopf_fibration
projection from a product manifold |
| gptkbp:field |
differential geometry
|
| gptkbp:generalizes |
Riemannian covering maps
|
| gptkbp:hasApplication |
construction of new Riemannian manifolds
study of curvature properties theory of harmonic maps theory of minimal submanifolds |
| gptkbp:hasProperty |
fibers are totally geodesic if and only if O'Neill's tensor A vanishes
|
| gptkbp:hasTensor |
O'Neill's tensor A
O'Neill's tensor T |
| https://www.w3.org/2000/01/rdf-schema#label |
Riemannian submersions
|
| gptkbp:introduced |
Barrett O'Neill
|
| gptkbp:introducedIn |
1966
|
| gptkbp:preserves |
length of horizontal vectors
|
| gptkbp:relatedTo |
gptkb:Riemannian_manifolds
gptkb:Riemannian_foliations submersion isometric submersions |
| gptkbp:studiedIn |
gptkb:global_Riemannian_geometry
|
| gptkbp:usedIn |
study of fiber bundles
study of homogeneous spaces |
| gptkbp:bfsParent |
gptkb:Riemannian_Geometry
|
| gptkbp:bfsLayer |
8
|