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By Barletta E., Dragomir S., Duggal K.L.
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Phys. 46 (1971) 1560; Derived also in unpublished lectures of Y. Nambu presented in Copenhagen, 1970. [9] D. R. Grigore, The variational sequence on finite order bundle extensions and the Lagrange formalism, Diff. Geom. Appl. 10 (1999) 43–77. [10] D. R. Grigore, Variationally trivial Lagrangians and locally variational equations of arbitrary order, Diff. Geom. Appl. 10 (1999) 79–105. [11] I. S. Krasilschik, V. V. Lychagin and A. M. Vinogradov, Geometry of Jet Spaces and Nonlinear Partial Differential Equations (Advanced Studies in Contemporary Mathematics 1, Gordon & Breach, New York, 1986).
Elsevier, Amsterdam, 2008) 773–836. [27] D. Krupka and J. Musilov´a, Trivial Lagrangians in Field Theory, Diff. Geom. and Appl. 9 (1998) 393–505. [28] D. Krupka and J. Musilov´a, Recent results in variational sequence theory, In: Steps in Differential Geometry (Proc. Colloq. Differential Geometry, Debrecen, Hungary, 2000, (L. Kozma, P. T. Nagy and L. ) Debrecen, 2001) 161–186. ˇ enkov´a, Variational sequences and Lepage forms, In: Differential [29] D. Krupka and J. Sedˇ Geometry and its Applications (Proc.
15) where ρ is any Lepage equivalent of λ. 14) into the term Θλ that is determined by the Lagrangian, and an auxiliary term p1 dν generally is not invariant under changes of fibred coordinates. 11) may have only a local meaning, not providing a differential form on J 2r−1 Y . If Θλ happens to be a global differential form, we speak about the (higher-order) Poincar´e–Cartan form associated to the Lagrangian λ, or, about the Poincar´e–Cartan equivalent of λ. Equipped with Lepage n-forms, we are able to write down the intrinsic first variation formula.