Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds
Differential Geometry
2008-12-18 v3
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.
Cite
@article{arxiv.0806.1632,
title = {Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds},
author = {Shirley Bromberg and Alberto Medina},
journal= {arXiv preprint arXiv:0806.1632},
year = {2008}
}
Comments
Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/