On the geometry of variational calculus on some functional bundles

Details On the geometry of variational calculus on some functional bundles On the geometry of variational calculus on some functional bundles

2004-07-19

arxiv.org/abs/math/0407320v1

Mathematics

Differential Geometry

Scientific paper

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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