Displaying similar documents to “Higher order contact of real curves in a real hyperquadric”

Higher order contact of real curves in a real hyperquadric. II

Yuli Villarroel (1998)

Archivum Mathematicum

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Let Φ be an Hermitian quadratic form, of maximal rank and index ( n , 1 ) , defined over a complex ( n + 1 ) vector space V . Consider the real hyperquadric defined in the complex projective space P n V by Q = { [ ς ] ∈ P n V , Φ ( ς ) = 0 } . Let G be the subgroup of the special linear group which leaves Q invariant and D the ( 2 n ) - distribution defined by the Cauchy Riemann structure induced over Q . We study the real regular curves of constant type in Q , tangent to D , finding a complete system of analytic invariants for two curves to be locally...

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,...