THE CARTAN FORM AND ITS GENERALIZATIONS IN THE CALCULUS OF VARIATIONS Academic Article uri icon

abstract

  • In this paper, we discuss possible extensions of the concept of the Cartan form of classical mechanics to higher-order mechanics on manifolds, higher-order field theory on jet bundles and to parametric variational problems on slit tangent bundles and on bundles of nondegenerate velocities. We present a generalization of the Cartan form, known as a Lepage form, and basic properties of the Lepage forms. Both earlier and recent examples of differential forms generalizing the Cartan form are reviewed.

authors

  • Rossi, Olga
  • KRUPKA, DEMETER
  • KRUPKOVÁ, OLGA
  • SAUNDERS, DAVID

publication date

  • June 2010