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A Goursat structure on a manifold of dimension $n$ is a rank two distribution $𝒟$ such that dim ${𝒟}^{\left(i\right)}=i+2$, for $0\le i\le n-2$, where ${𝒟}^{\left(i\right)}$ denote the elements of the derived flag of $𝒟$, defined by ${𝒟}^{\left(0\right)}=𝒟$ and ${𝒟}^{(i+1)}={𝒟}^{\left(i\right)}+[{𝒟}^{\left(i\right)},{𝒟}^{\left(i\right)}]$. 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, called...

A Goursat structure on a manifold of dimension is a rank two distribution such that dim = + 2, for 0 ≤ ≤ -2, where denote the elements of the derived flag of , defined by = and = + [ , ] . 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...