abstract: In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian to Hamiltonian classical field theories, and then we reformulate the latter in multisymplectic terms. Furthermore, we investigate basic questions on normal forms of multisymplectic manifolds, notably the questions wether and when Darboux-type theorems hold, and how many diffeomorphisms certain, important classes of multisymplectic manifolds possess. Finally, we survey recent advances in the area of symmetries and conserved quantities on multisymplectic manifolds.

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@article{Ryvkin-An-invitation-to-2019,
 abstract = {In this article we study multisymplectic geometry, i.e., the geometry of
manifolds with a non-degenerate, closed differential form. First we describe
the transition from Lagrangian to Hamiltonian classical field theories, and
then we reformulate the latter in multisymplectic terms. Furthermore, we
investigate basic questions on normal forms of multisymplectic manifolds,
notably the questions wether and when Darboux-type theorems hold, and how many
diffeomorphisms certain, important classes of multisymplectic manifolds
possess. Finally, we survey recent advances in the area of symmetries and
conserved quantities on multisymplectic manifolds.},
 author = {Ryvkin, Leonid and Wurzbacher, Tilmann},
 doi = {10.1016/j.geomphys.2019.03.006},
 eprint = {1804.02553},
 fjournal = {Journal of Geometry and Physics},
 issn = {0393-0440},
 journal = {J. Geom. Phys.},
 keywords = {53D05,70S05,37C05,53D20,37K05},
 language = {English},
 pages = {9--36},
 title = {An invitation to multisymplectic geometry},
 volume = {142},
 year = {2019},
 zbl = {1416.53076},
 zbmath = {7068171}
}