Geodesic
Variational principles and symmetries on fibered multisymplectic manifolds
Communications in Mathematics, Tome 24 (2016) no. 2, pp. 137-152 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multisymplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special cases, first and higher order field theories and (non-autonomous) mechanics.
The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multisymplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special cases, first and higher order field theories and (non-autonomous) mechanics.
Classification : 49S05, 53D42, 55R10, 70H50, 70S05, 70S10
Keywords: Variational principles; Symmetries; Conserved quantities; Noether theorem; Fiber bundles; Multisymplectic manifolds. 
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Gaset, Jordi; Prieto-Martínez, Pedro D.; Román-Roy, Narciso. Variational principles and symmetries on fibered multisymplectic manifolds. Communications in Mathematics, Tome 24 (2016) no. 2, pp. 137-152. http://geodesic.mathdoc.fr/item/COMIM_2016_24_2_a4/

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