THE CARTAN FORM AND ITS GENERALIZATIONS IN THE CALCULUS OF VARIATIONS
| Authors | |
|---|---|
| Year of publication | 2010 |
| Type | Article in Periodical |
| Magazine / Source | International Journal of Geometric Methods in Modern Physics |
| MU Faculty or unit | |
| 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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