# Lagrangian Submanifolds of Standard Multisymplectic Manifolds

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## 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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