On the normal forms for Pfaffian systems

Abstract

We discuss local normal forms of Pfaffian systems and obtain a necessary and sufficient condition, in terms of relative polarizations, for the local generators of a Pfaffian system to convert to the contact system on the jet manifold $J^r(\R^h,\R^q)$, or to the Pfaffian system associated to a system of partial differential equations. This result generalizes the Darboux theorem on a Pfaffian equation of constant class.