by M. Marvan
Geometrical Methods in Physics, Proc. Conf. on Differential Geometry and its Applications, Nove Mesto na Morave, Sept. 5–9, 1983 (J.E. Purkyne Univ., Brno, 1984) 185–190.
The sheaf of lepagean equivalents of the zero lagrangian on a fibred manifold is shown to be fine. In this way, the existence of a global first-variation formula of the calculus of variations on fibred manifolds is established by a sheaf-theoretical method. Earlier the existence of the global first-variation formula was proved by different methods by B.A. Kupershmidt (1980); D. Krupka (1982); M. Horak and I. Kolar; P.L. Garcia and J. Munoz.