THE CARTAN FORM AND ITS GENERALIZATIONS IN THE CALCULUS OF VARIATIONS

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Authors

KRUPKA Demeter KRUPKOVÁ Olga SAUNDERS David

Year of publication 2010
Type Article in Periodical
Magazine / Source International Journal of Geometric Methods in Modern Physics
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1142/S0219887810004488
Field General mathematics
Keywords Fibered manifold; calculus of variations; first variation formula; Cartan form; Lepage form
Description 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
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