On the contact and co-contact of higher order

A. Mastromartino and Y. Nogier

Abstract: The unifying methodologies are based on the construction of ‘bridges’ connecting distinct mathematical theories with each other. The purpose of this paper is to study the relationship between the geometric and algebraic formulation of completely integrable systems of order $k$ and dimension $n$ over a differentiable manifold, in terms of contact $C^{k,n}M$ and co-contact ${\left(C^{k,n}M\right)}^0$ of higher order, as seen in [A. Morimoto, Prolongation of Geometric Structures, Math. Inst. Nagoya University, Nagoya, (1969)], to establish an equivalence between both formulations.

Keywords: geometric structures on manifolds; differential systems; contact theory; co-contact of higher order

Classification (MSC2000): 53C15; 53B25

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