Some maximal isotropic distributions and their relation to field theory

TL;DR

This paper investigates the structure of differential forms with maximal isotropic distributions, providing a decomposition under certain conditions and classifying canonical coordinates relevant to classical field theory.

Contribution

It introduces a decomposition method for differential forms with isotropic distributions and classifies canonical coordinates, advancing understanding in geometric field theory.

Findings

Forms can be decomposed into constant and vanishing parts under integrability conditions.

Classification of canonical coordinates for specific forms.

Potential applications in classical field theory.

Abstract

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.