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'.

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@misc{Ryvkin-Darboux-type-theorems-2025,
 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'.},
 arxiv = {arXiv:2503.03672},
 author = {Ryvkin, Leonid},
 eprint = {2503.03672},
 howpublished = {Preprint, {arXiv}:2503.03672 [math.{SG}] (2025)},
 keywords = {53C15,53C10,53D05},
 title = {Darboux type theorems in multisymplectic geometry},
 url = {https://arxiv.org/abs/2503.03672},
 year = {2025}
}