Geodesic
Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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In this work it is shown that a necessary condition for the 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.
Keywords: Lorentzian metrics; complete geodesics; 3-dimensional Lie groups
Mots-clés : Euler equation. 
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     author = {Shirley Bromberg and Alberto Medina},
     title = {Geodesically {Complete} {Lorentzian} {Metrics} on {Some} {Homogeneous} {3~Manifolds}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a87/}
}
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Shirley Bromberg; Alberto Medina. Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a87/

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