Some maximal isotropic distributions and their relation to field theory

We study the behaviour of differential forms in a manifold having at least one of their maximal isotropic local distributions endowed with the special algebraic property of being decomposable. We show that they can be represented as the sum of a form with constant coefficients and one that vanishes whenever contracted with vector fields in the former distribution, provided some simple integrability conditions are ensured. We also classify possible ‘canonical coordinates’ for a certain class of forms with potential applications in classical field theory.