A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold
| dc.creator | Sarlet, Willy | |
| dc.date | 2007-02-13 | |
| dc.date.accessioned | 2026-07-07T09:34:35Z | |
| dc.date.available | 2026-07-07T09:34:35Z | |
| dc.description | We review properties of so-called special conformal Killing tensors on a Riemannian manifold $(Q,g)$ and the way they give rise to a Poisson-Nijenhuis structure on the tangent bundle $TQ$. We then address the question of generalizing this concept to a Finsler space, where the metric tensor field comes from a regular Lagrangian function $E$, homogeneous of degree two in the fibre coordinates on $TQ$. It is shown that when a symmetric type (1,1) tensor field $K$ along the tangent bundle projection $τ: TQ\to Q$ satisfies a differential condition which is similar to the defining relation of special conformal Killing tensors, there exists a direct recursive scheme again for first integrals of the geodesic spray. Involutivity of such integrals, unfortunately, remains an open problem. | |
| dc.description | This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/math/0702383 | |
| dc.identifier | http://arxiv.org/abs/math/0702383 | |
| dc.identifier | SIGMA 3 (2007), 024, 9 pages | |
| dc.identifier | doi:10.3842/SIGMA.2007.024 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159544 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.title | A Recursive Scheme of First Integrals of the Geodesic Flow of a Finsler Manifold | |
| dc.type | text |