Géométrie des groupes oscillateurs et variétés localement symétriques

2002/04/01 by Shirley Bromberg, Bromberg, Shirley, Alberto Medina +1
Mathematics · #14R99 #53C35 #53C50 #53D25 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:14R99 #msc:53C35 #msc:53C50 #msc:53D25

paper · pdf · doi:10.48550/arxiv.math/0204019

arxiv created 2002/04/01 · arxiv updated 2009/11/30

Abstract

The Oscillator Groups,\G_λ, are the only solvable, non commutative, simply connected Lie groups to admit a Lorentzian bi-invariant metric. For these groups, we give sufficient conditions for a left-invariant pseudo-Riemannian metric to be complete, we determine the group of isometries, we exhibit a left-invariant affine structure and prove that it is not Lorentzian. As an application, we provide new examples of compact pseudo-Riemannian (sometimes Lorentzian) locally symmetric, occasionally affine, manifolds, complete or incomplete.

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