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Géométrie des groupes oscillateurs et variétés localement symétriques

Shirley Bromberg·Alberto Medina
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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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Shirley Bromberg, Alberto Medina. 2002-04-01. Géométrie des groupes oscillateurs et variétés localement symétriques. https://arxiv.org/abs/math/0204019

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