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On the geometry of Goursat structures

William Pasillas-Lépine, Witold Respondek (2001)

ESAIM: Control, Optimisation and Calculus of Variations

A Goursat structure on a manifold of dimension n is a rank two distribution 𝒟 such that dim 𝒟 ( i ) = i + 2 , for 0 i 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, called...

On the Geometry of Goursat Structures

William Pasillas-Lépine, Witold Respondek (2010)

ESAIM: Control, Optimisation and Calculus of Variations

A Goursat structure on a manifold of dimension n is a rank two distribution Ɗ such that dim Ɗ(i) = i + 2, for 0 ≤ i ≤ n-2, where Ɗ(i) denote the elements of the derived flag of Ɗ, defined by Ɗ(0) = Ɗ and Ɗ(i+1) = Ɗ(i) + [Ɗ(i),Ɗ(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...

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