Displaying similar documents to “Characteristic vector fields of generic distributions of corank 2”

On the geometry of Goursat structures

William Pasillas-Lépine, Witold Respondek (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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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 ≤ 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,...

Congruent numbers over real number fields

Tomasz Jędrzejak (2012)

Colloquium Mathematicae

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It is classical that a natural number n is congruent iff the rank of ℚ -points on Eₙ: y² = x³-n²x is positive. In this paper, following Tada (2001), we consider generalised congruent numbers. We extend the above classical criterion to several infinite families of real number fields.