Displaying similar documents to “Geometric approach to Goursat flags”

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

Mohamad Cheaito, Piotr Mormul (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

Generic one-step bracket-generating distributions of rank four

Chiara De Zanet (2015)

Archivum Mathematicum

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We give a uniform, explicit description of the generic types of one–step bracket–generating distributions of rank four. A manifold carrying such a structure has dimension at least five and no higher than ten. For each of the generic types, we give a brief description of the resulting class of generic distributions and of geometries equivalent to them. For dimensions different from eight and nine, these are available in the literature. The remaining two cases are dealt with in my doctoral...

A rigidity phenomenon for germs of actions of R 2

Aubin Arroyo, Adolfo Guillot (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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We study germs of Lie algebras generated by two commuting vector fields in manifolds that are in the sense of Palais (those which do not present any evident obstruction to be the local model of an action of  R 2 ). We study three particular pairs of homogeneous quadratic commuting vector fields (in  R 2 , R 3 and  R 4 ) and study the maximal Lie algebras generated by commuting vector fields whose 2-jets at the origin are the given homogeneous ones. In the first case we prove that the quadratic algebra...

Split octonions and generic rank two distributions in dimension five

Katja Sagerschnig (2006)

Archivum Mathematicum

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In his famous five variables paper Elie Cartan showed that one can canonically associate to a generic rank 2 distribution on a 5 dimensional manifold a Cartan geometry modeled on the homogeneous space G ˜ 2 / P , where P is one of the maximal parabolic subgroups of the exceptional Lie group G ˜ 2 . In this article, we use the algebra of split octonions to give an explicit global description of the distribution corresponding to the homogeneous model.