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A rigidity phenomenon for germs of actions of R 2

Aubin Arroyo, Adolfo 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 maximal 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...

Comparison of metrics on three-dimensional Lie groups

Federico G. Lastaria (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study local equivalence of left-invariant metrics with the same curvature on Lie groups G and G ¯ of dimension three, when G is unimodular and G ¯ is non-unimodular.

On Riemann-Poisson Lie groups

Brahim Alioune, Mohamed Boucetta, Ahmed Sid’Ahmed Lessiad (2020)

Archivum Mathematicum

A Riemann-Poisson Lie group is a Lie group endowed with a left invariant Riemannian metric and a left invariant Poisson tensor which are compatible in the sense introduced in [4]. We study these Lie groups and we give a characterization of their Lie algebras. We give also a way of building these Lie algebras and we give the list of such Lie algebras up to dimension 5.

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