The Euler-Lagrange PDE and Finsler metrizability
| dc.creator | Muzsnay, Zoltan | |
| dc.date | 2006-02-17 | |
| dc.date.accessioned | 2026-07-07T07:03:33Z | |
| dc.date.available | 2026-07-07T07:03:33Z | |
| dc.description | In this paper we investigate the following question: under what conditions can a second-order homogeneous ordinary differential equation (spray) be the geodesic equation of a Finsler space. We show that the Euler-Lagrange partial differential system on the energy function can be reduced to a first order system on this same function. In this way we are able to give effective necessary and sufficient conditions for the local existence of a such Finsler metric in terms of the holonomy algebra generated by horizontal vector-fields. We also consider the Landsberg metrizability problem and prove similar results. This reduction is a significant step in solving the problem whether or not there exists a non-Berwald Landsberg space. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0602383 | |
| dc.identifier | http://arxiv.org/abs/math/0602383 | |
| dc.identifier | Houston Journal of Mathematics, 32, no1, 2006, pp. 79-98 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109012 | |
| dc.subject | Differential Geometry | |
| dc.subject | 49N45; 35N10; 53C60; 53B05 | |
| dc.title | The Euler-Lagrange PDE and Finsler metrizability | |
| dc.type | text |