  We give necessary and sufficient geometric conditions for a distribution (or
a Pfaffian system) to be locally equivalent to the canonical contact system on
Jn(R,Rm), the space of n-jets of maps from R into Rm. 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
Jn(R,Rm) in a way analogous to that how Kumpera-Ruiz normal form generalizes
the canonical contact system on Jn(R,R), which is also called Goursat normal
form.
