Darboux type theorems in multisymplectic geometry
Symplectic Geometry
2025-06-26 v3
Abstract
We give a survey of Darboux type theorems in multisymplectic geometry. These theorems establish when a closed differential form of a certain type admits a constant-coefficient expression in some local coordinate system. Beyond the classical cases of symplectic and volume forms, 0-deformability (i.e. constancy of linear type) is typically not automatic and has to be imposed, leading to distinct theorems 'per linear type'.
Cite
@article{arxiv.2503.03672,
title = {Darboux type theorems in multisymplectic geometry},
author = {Leonid Ryvkin},
journal= {arXiv preprint arXiv:2503.03672},
year = {2025}
}
Comments
This article supersedes arXiv:1609.02184 and the authors Phd thesis, and has significant text overlap with these works. v2: typos corrected, result on codegree 2 forms added (section 3.6)