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By Krupka D., et al. (eds.)
This booklet is a suite of survey articles in a extensive box of the geometrical concept of the calculus of adaptations and its functions in research, geometry and physics. it's a commemorative quantity to rejoice the sixty-fifth birthday of Professor Krupa, one of many founders of recent geometric variational concept, and a huge contributor to this subject and its purposes during the last thirty-five years. the entire authors invited to give a contribution to this quantity have confirmed excessive reputations of their box. The booklet will completely offer a number of very important effects, ideas and functions which are frequently on hand in simple terms via consulting unique papers in lots of various journals. will probably be of curiosity to researchers in variational calculus, mathematical physics and the opposite comparable components of differential equations, usual operators and geometric constructions. additionally, it's going to develop into an enormous resource of present examine for doctoral scholars and postdoctorals in those fields.
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Extra info for Variations, geometry and physics, In honour of Demeter Krupka's 65 birthday
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Phys. 46 (1971) 1560; Derived also in unpublished lectures of Y. Nambu presented in Copenhagen, 1970.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.