On the geometry of variational calculus on some functional bundles

Authors

  • Antonella Cabras
  • Josef Janyška
  • Ivan Kolàr

DOI:

https://doi.org/10.1285/i15900932v26n2p51

Keywords:

Formal exterior differential, Bundle of smooth maps, Operator order of a morphism, Fiberwise $...$-jet, Euler-Lagrange morphism

Abstract

We first generalize the operation of formal exterior differential in the case of finite dimensional fibered manifolds and then we extend it to certain bundles of smooth maps. In order to characterize the operator order of some morphisms between our bundles of smooth maps, we introduce the concept of fiberwise $(k,r)$-jet. The relations to the Euler-Lagrange morphism of the variational calculus are described.

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Published

01-10-2006

Issue

Volume 26, Issue 2 (2006)

Section

Articoli

License

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http://creativecommons.org/licenses/by-nc-nd/3.0/it/legalcode