Abstract

The integrability of the Euler–Lagrange equations and the Jacobi fields of the natural basis of Lagrangian densities on the bundle of linear frames of a manifold which are invariant under diffeomorphisms, is stated. Applications to the reducibility of the pre-symplectic structure attached to such variational problems as defined in [Symp. Math. 14 (1974) 219], are also given.

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