Higher order Grassmann fibrations and the calculus of variations

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Authors

KRUPKA Demeter KRUPKA Michal

Year of publication 2010
Type Article in Periodical
Magazine / Source Balkan Journal of Geometry and its Applications
MU Faculty or unit

Faculty of Science

Citation
Field General mathematics
Keywords Variational theory; velocity bundle; Grassmann bundle; Lepage form
Description Geometric structure of global integral variational functionals on higher order tangent bundles and Grassmann fibrations are investigated. The theory of Lepage forms is extended to these structures. The concept of a Lepage form allows us to introduce the Euler-Lagrange distribution for variational functionals, depending on velocities, in a similar way as in the calculus of variations on fibred manifolds. Integral curves of this distribution include all extremal curves of the underlying variational functional. The generators of the Euler-Lagrange distribution, defined by the Lepage forms of the first order, are found explicitly
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