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Some Properties of Multisymplectic Manifolds

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Classical and Quantum Physics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 229))

Abstract

This lecture is devoted to review some of the main properties of multisymplectic geometry.  In particular, after reminding the standard definition of multisymplectic manifold, we introduce its characteristic submanifolds, the canonical models, and other relevant kinds of multisymplectic manifolds, such as those where the existence of Darboux-type coordinates is assured. The Hamiltonian structures that can be defined in these manifolds are also studied, as well as other important properties, such as their invariant forms and the characterization by automorphisms.

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Acknowledgements

I acknowledge the financial support of the Ministerio de Ciencia e Innovación (Spain), projects MTM2014–54855–P and MTM2015-69124–REDT, and of Generalitat de Catalunya, project 2017–SGR–932.

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Authors and Affiliations

  1. Department of Mathematics, Ed. C-3, Campus Norte UPC, C/ Jordi Girona 1, 08034, Barcelona, Spain

    Narciso Román-Roy

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  1. Narciso Román-Roy
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Correspondence to Narciso Román-Roy .

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Editors and Affiliations

  1. Università degli Studi di Napoli Federico II, Naples, Italy

    G. Marmo

  2. Institute of Mathematical Sciences (ICMAT), Madrid, Spain

    David Martín de Diego

  3. Universitat Politècnica de Catalunya, Barcelona, Spain

    Miguel Muñoz Lecanda

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Román-Roy, N. (2019). Some Properties of Multisymplectic Manifolds. In: Marmo, G., Martín de Diego, D., Muñoz Lecanda, M. (eds) Classical and Quantum Physics. Springer Proceedings in Physics, vol 229. Springer, Cham. https://doi.org/10.1007/978-3-030-24748-5_18

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