| 1. | The theory of isoparametric submanifolds is deeply related to the theory of holonomy groups.
|
| 2. | Lifts of loops about a point give rise to the holonomy group at that point.
|
| 3. | If F has a holonomy group then every leaf of F is compact with finite holonomy group ."
|
| 4. | If F has a holonomy group then every leaf of F is compact with finite holonomy group ."
|
| 5. | See below . ) It is now known that all of these possibilities occur as holonomy groups of Riemannian manifolds.
|
| 6. | It was not until much later that holonomy groups would be used to study Riemannian geometry in a more general setting.
|
| 7. | The paper " Submanifolds with constant principal curvatures and normal holonomy groups " is a very good introduction to such theory.
|
| 8. | As with the holonomy groups, the holonomy bundle also transforms equivariantly within the ambient principal bundle " P ".
|
| 9. | Theorem : " Let F be a holonomy group, then all the leaves of F are compact with finite holonomy group ."
|
| 10. | Theorem : " Let F be a holonomy group, then all the leaves of F are compact with finite holonomy group ."
|
मोबाइल