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Communications in Mathematics

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Variational principles and symmetries on fibered multisymplectic manifolds

Jordi Gaset
  • Corresponding author
  • Department of Mathematics. Ed. C-3, Campus Norte UPC C/ Jordi Girona 1. 08034 Barcelona, Spain
  • Email:
/ Pedro D. Prieto-Martínez
  • Department of Mathematics. Ed. C-3, Campus Norte UPC C/ Jordi Girona 1. 08034 Barcelona, Spain
  • Email:
/ Narciso Román-Roy
  • Department of Mathematics. Ed. C-3, Campus Norte UPC C/ Jordi Girona 1. 08034 Barcelona, Spain
  • Email:
Published Online: 2016-12-22 | DOI: https://doi.org/10.1515/cm-2016-0010

Abstract

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.

Keywords: Variational principles; Symmetries; Conserved quantities; Noether theorem; Fiber bundles; Multisymplectic manifolds

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About the article

Received: 2016-10-17

Accepted: 2016-12-06

Published Online: 2016-12-22

Published in Print: 2016-12-01


Citation Information: Communications in Mathematics, ISSN (Online) 2336-1298, DOI: https://doi.org/10.1515/cm-2016-0010. Export Citation

© 2016. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. (CC BY-NC-ND 4.0)

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