English

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 c0,1c \neq 0, 1 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