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A rigidity phenomenon for germs of actions of R 2

Aubin ArroyoAdolfo Guillot — 2010

Annales de la faculté des sciences de Toulouse Mathématiques

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 is a smooth...

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