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Article Dans Une Revue Symmetry, Integrability and Geometry : Methods and Applications Année : 2008

Geodesically Complete Lorentzian metrics on some Homogeneous 3 manifolds

Shirley Bromberg
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Résumé

It is shown that a necessary condition for completeness of the geodesics of left invariant pseudo-Riemannian metrics on Lie groups is also sufficient in the case of 3-dimensional unimodular Lie groups and not sufficient for 3-dimensional non unimodular Lie groups. As a consequence it is possible to identify, amongst the compact locally homogeneous Lorentzian 3-manifolds with non compact (local) isotropy group, those that are geodesically complete.
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Dates et versions

hal-00821118 , version 1 (07-05-2013)

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Shirley Bromberg, Alberto Medina. Geodesically Complete Lorentzian metrics on some Homogeneous 3 manifolds. Symmetry, Integrability and Geometry : Methods and Applications, 2008, 4, Open journal online. ⟨10.3842/SIGMA.2008.088⟩. ⟨hal-00821118⟩
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