Exactness of Lepage 2-forms and globally variational differential equations
Differential Geometry
2020-04-02 v1
Abstract
The exactness equation for Lepage 2-forms, associated with variational systems of ordinary differential equations on smooth manifolds, is analyzed with the aim to construct a concrete global variational principle. It is shown that locally variational systems defined by homogeneous functions of degree are automatically globally variational. A new constructive method of finding a global Lagrangian is described for these systems, which include for instance the geodesic equations in Riemann and Finsler geometry.
Keywords
Cite
@article{arxiv.1909.05115,
title = {Exactness of Lepage 2-forms and globally variational differential equations},
author = {Zbynek Urban and Jana Volna},
journal= {arXiv preprint arXiv:1909.05115},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1812.04270