On the contact and co-contact of higher order

Abstract

The unifying methodologies are based on theconstruction of `bridges' connecting distinct mathematicaltheories with each other. The purpose of this paper is to studythe relationship between the geo\-me\-tric and algebraicformulation of completely integrable systems of order $k$ anddimension $n$ over a differentiable manifold, in terms of contact$C^{k,n}M$ and co-contact $(C^{k,n}M)^0$ of higher order, as seenin [A. Morimoto, {Prolongation of Geometric Structures}, Math. Inst. Nagoya University, Nagoya, (1969)], to establish an equivalence between bothformulations.