Characteristic vector fields of generic distributions of corank 2

B. Jakubczyk; W. Kryński; F. Pelletier

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A Goursat structure on a manifold of dimension $n$ is a rank two distribution $𝒟$ such that dim $𝒟^{(i)} = i + 2$ , for $0 \leq i \leq n - 2$ , where $𝒟^{(i)}$ denote the elements of the derived flag of $𝒟$ , defined by $𝒟^{(0)} = 𝒟$ and $𝒟^{(i + 1)} = 𝒟^{(i)} + [𝒟^{(i)}, 𝒟^{(i)}]$ . Goursat structures appeared first in the work of von Weber and Cartan, who have shown that on an open and dense subset they can be converted into the so-called Goursat normal form. Later, Goursat structures have been studied by Kumpera and Ruiz. In the paper, we introduce a new local invariant for Goursat structures,...

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