Higher order Grassmann fibrations and the calculus of variations
| Authors | |
|---|---|
| Year of publication | 2010 |
| Type | Article in Periodical |
| Magazine / Source | Balkan Journal of Geometry and its Applications |
| MU Faculty or unit | |
| 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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