Darboux type theorems in multisymplectic geometry

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'.

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)