Contact systems and corank one involutive subdistributions

Details Contact systems and corank one involutive subdistributions Contact systems and corank one involutive subdistributions

2000-04-19

arxiv.org/abs/math/0004124v1

Mathematics

Differential Geometry

LaTeX2e, 29 pages, submitted to Acta applicandae mathematicae

Scientific paper

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.

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