The Euler-Lagrange PDE and Finsler metrizability
Differential Geometry
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0602383,
title = {The Euler-Lagrange PDE and Finsler metrizability},
author = {Zoltan Muzsnay},
journal= {arXiv preprint arXiv:math/0602383},
year = {2007}
}
Comments
20 pages