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arXiv · 0806.1632

Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds

Shirley Bromberg·Alberto Medina
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Abstract

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.

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Shirley Bromberg, Alberto Medina. 2008-12-18. Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds. https://doi.org/10.3842/sigma.2008.088

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