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.
@article{701697,
title = {Generalized Jacobi morphisms in variational sequences},
booktitle = {Proceedings of the 21st Winter School "Geometry and Physics"},
series = {GDML\_Books},
publisher = {Circolo Matematico di Palermo},
address = {Palermo},
year = {2002},
pages = {[195]-208},
mrnumber = {MR1972435},
zbl = {1028.58022},
url = {http://dml.mathdoc.fr/item/701697}
}
Francaviglia, Mauro; Palese, Marcella. Generalized Jacobi morphisms in variational sequences, dans Proceedings of the 21st Winter School "Geometry and Physics", GDML_Books, (2002), pp. [195]-208. http://gdmltest.u-ga.fr/item/701697/