Pfaffian system

Summary

A Pfaffian system is an exterior differential system generated by one-forms. Equivalently, it is given by a field of linear conditions on tangent vectors, that is, by a distribution, the common kernel of the generating forms. Its integral manifolds are the submanifolds tangent to this distribution. The Frobenius theorem tells exactly when the integral manifolds fill out the manifold as the leaves of a foliation.