Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds

Details Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds

2008-06-10

arxiv.org/abs/0806.1632v3

SIGMA 4 (2008), 088, 13 pages

Mathematics

Differential Geometry

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2008.088

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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