Variational principles and symmetries on fibered multisymplectic manifolds

Jordi Gaset 1 , Pedro D. Prieto-Martínez 1 , and Narciso Román-Roy 1
  • 1 Department of Mathematics. Ed. C-3, Campus Norte UPC C/ Jordi Girona 1. 08034 Barcelona, Spain


The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multi-symplectic 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.

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