On the intrinsic geometry of a unit vector field
| dc.creator | Yampolsky, Alexander | |
| dc.date | 2005-03-24 | |
| dc.date.accessioned | 2026-07-07T05:18:25Z | |
| dc.date.available | 2026-07-07T05:18:25Z | |
| dc.description | We study the geometrical properties of a unit vector field on a Riemannian 2-manifold, considering the field as a local imbedding of the manifold into its tangent sphere bundle with the Sasaki metric. For the case of constant curvature K, we give a description of the totally geodesic unit vector fields for K=0 and K=1 and prove a non-existence result for K not equal to 0 and 1. We also found a family of vector fields on the hyperbolic 2-plane L^2 of curvature -c^2 which generate foliations on unit tangent bundle over L^2 with leaves of constant intrinsic curvature -c^2 and of constant extrinsic curvature -c^2/4. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0503565 | |
| dc.identifier | http://arxiv.org/abs/math/0503565 | |
| dc.identifier | Comment. Mat. Univ. Carolinae 43, 2 (2002), 299-317 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74653 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53B25, 53C25 | |
| dc.title | On the intrinsic geometry of a unit vector field | |
| dc.type | text |