An Inverse Problem from Sub-Riemannian Geometry
| dc.creator | Ivey, Thomas A. | |
| dc.date | 2001-04-14 | |
| dc.date.accessioned | 2026-07-07T04:41:19Z | |
| dc.date.available | 2026-07-07T04:41:19Z | |
| dc.description | The geodesics for a sub-Riemannian metric on a three-dimensional contact manifold $M$ form a 1-parameter family of curves along each contact direction. However, a collection of such contact curves on $M$, locally equivalent to the solutions of a fourth-order ODE, are the geodesics of a sub-Riemannian metric only if a sequence of invariants vanish. The first of these, which was earlier identified by Fels, determines if the differential equation is variational. The next two determine if there is a well-defined metric on $M$ and if the given paths are its geodesics. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0104157 | |
| dc.identifier | http://arxiv.org/abs/math/0104157 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61311 | |
| dc.subject | Differential Geometry | |
| dc.subject | Optimization and Control | |
| dc.subject | 53C17;49N45 (Primary) 34A26;53A55 (Secondary) | |
| dc.title | An Inverse Problem from Sub-Riemannian Geometry | |
| dc.type | text |