On special types of minimal and totally geodesic unit vector fields
| dc.creator | Yampolsky, Alexander | |
| dc.date | 2005-09-30 | |
| dc.date.accessioned | 2026-07-07T06:20:31Z | |
| dc.date.available | 2026-07-07T06:20:31Z | |
| dc.description | We present a new equation with respect to a unit vector field on Riemannian manifold $M^n$ such that its solution defines a totally geodesic submanifold in the unit tangent bundle with Sasaki metric and apply it to some classes of unit vector fields. We introduce a class of covariantly normal unit vector fields and prove that within this class the Hopf vector field is a unique global one with totally geodesic property. For the wider class of geodesic unit vector fields on a sphere we give a new necessary and sufficient condition to generate a totally geodesic submanifold in $T_1S^n$. | |
| dc.description | 15 Pages | |
| dc.identifier | https://arxiv.org/abs/math/0510002 | |
| dc.identifier | http://arxiv.org/abs/math/0510002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95345 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53B20, 53B25; 53C25 | |
| dc.title | On special types of minimal and totally geodesic unit vector fields | |
| dc.type | text |