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Generalized Jacobi morphisms in variational sequences. (English) Zbl 1028.58022
Slovák, Jan (ed.) et al., The proceedings of the 21th winter school “Geometry and physics”, Srní, Czech Republic, January 13-20, 2001. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 69, 195-208 (2002).
Summary: We provide a geometric interpretation of generalized Jacobi morphisms in the framework of finite order variational sequences.
Jacobi morphisms arise classically as an outcome of an invariant decomposition of the second variation of a Lagrangian. Here they are characterized in the context of generalized Lagrangian symmetries in terms of variational Lie derivatives of generalized Euler-Lagrange morphisms. We introduce the variational vertical derivative and stress its link with the classical concept of variation. The relation with generalized Helmholtz morphisms is also clarified.
For the entire collection see [Zbl 0994.00029].

MSC:
 58E30 Variational principles in infinite-dimensional spaces 55R10 Fiber bundles in algebraic topology 58A12 de Rham theory in global analysis 58A20 Jets in global analysis 55N30 Sheaf cohomology in algebraic topology 70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems 70S10 Symmetries and conservation laws in mechanics of particles and systems