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Lagrangian Submanifolds of Standard Multisymplectic Manifolds

Conference paper
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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 290)

Abstract

We give a detailed, self-contained proof of Geoffrey Martin’s normal form theorem for Lagrangian submanifolds of standard multisymplectic manifolds (that generalises Alan Weinstein’s famous normal form theorem in symplectic geometry), providing also complete proofs for the necessary results in foliated differential topology, i.e., a foliated tubular neighborhood theorem and a foliated relative Poincaré lemma.

Keywords

Multisymplectic geometry Lagrangian submanifolds Foliated differential topology 

MSC (2010)

Primary: 53D05 53D12 Secondary: 53C12 

Notes

Acknowledgements

We wish to thank Camille Laurent-Gengoux for several useful discussions related to the content of this article.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institut Élie Cartan Lorraine, Université de Lorraine et C.N.R.S.MetzFrance

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