THE CARTAN FORM AND ITS GENERALIZATIONS IN THE CALCULUS OF VARIATIONS
| Autoři | |
|---|---|
| Rok publikování | 2010 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | International Journal of Geometric Methods in Modern Physics |
| Fakulta / Pracoviště MU | |
| Citace | |
| Doi | http://dx.doi.org/10.1142/S0219887810004488 |
| Obor | Obecná matematika |
| Klíčová slova | Fibered manifold; calculus of variations; first variation formula; Cartan form; Lepage form |
| Popis | 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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