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Rank-2 distributions satisfying the Goursat condition: all their local models in dimension 7 and 8

Published online by Cambridge University Press:  15 August 2002

Mohamad Cheaito  and
Piotr Mormul
Mohamad Cheaito
Affiliation:
Laboratoire E. Picard, U.M.R. C.N.R.S. 5580, Département de Mathématiques, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France; [email protected].
Piotr Mormul
Affiliation:
Instytut Matematyki, Uniwersytet Warszawski, Banacha 2, 02-097 Warszawa, Poland; [email protected].
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Abstract

We study the rank–2 distributions satisfying so-called Goursat condition (GC); that is to say, codimension–2 differential systems forming with their derived systems a flag. Firstly, we restate in a clear way the main result of[7] giving preliminary local forms of such systems. Secondly – and this is the main part of the paper – in dimension 7 and 8 we explain which constants in those local forms can be made 0, normalizing the remaining ones to 1. All constructed equivalences are explicit. The complete list of local models in dimension 7 contains 13 items, and not 14, as written in[7], while the list in dimension 8 consists of 34 models (and not 41, as could be concluded from some statements in[7]). In these dimensions (and in lower dimensions, too) the models are eventually discerned just by their small growth vector at the origin.

Keywords

DistributionGoursat conditionflagderived systemsmall growth vector.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 4 , 1999 , pp. 137 - 158
Copyright
© EDP Sciences, SMAI, 1999

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