Contact Systems and Corank One Involutive Subdistributions

Abstract

We give necessary and sufficient geometric conditions for a distribution (or a Pfaffian system) to be locally equivalent to the canonical contact system on J n (R,R m ). We study the geometry of that class of systems, in particular, the existence of corank one involutive subdistributions. We also distinguish regular points, at which the system is equivalent to the canonical contact system, and singular points, at which we propose a new normal form that generalizes the canonical contact system on J n (R,R m ) in a way analogous to that how the Kumpera–Ruiz normal form generalizes the canonical contact system on J n (R,R), which is also called the Goursat normal form.