On geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 1
| dc.creator | Zelenko, Igor | |
| dc.date | 2004-06-07 | |
| dc.date.accessioned | 2026-07-07T05:08:56Z | |
| dc.date.available | 2026-07-07T05:08:56Z | |
| dc.description | The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new elementary proof of classical Levi-Civita's Theorem about the classification of all Riemannian geodesically equivalent metrics in a neighborhood of so-called regular (stable) point w.r.t. these metrics. Secondly we prove that sub-Riemannian metrics on contact distributions are geodesically equivalent iff they are constantly proportional. Then we describe all geodesically equivalent sub-Riemannian metrics on quasi-contact distributions. Finally we make the classification of all pairs of geodesically equivalent Riemannian metrics on a surface, which proportional in an isolated point. This is the simplest case, which was not covered by Levi-Civita's Theorem. | |
| dc.description | 30 pages, to appear in "Journal of Mathematical Sciences" | |
| dc.identifier | https://arxiv.org/abs/math/0406111 | |
| dc.identifier | http://arxiv.org/abs/math/0406111 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71457 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C17, 53D25 | |
| dc.title | On geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 1 | |
| dc.type | text |