Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three

✍ Scribed by Calvaruso, G.; Marinosci, R. A.

• Book ID: 121310826
• Publisher: Walter de Gruyter GmbH & Co. KG
• Year: 2008
• Tongue: English
• Weight: 214 KB
• Volume: 8
• Category: Article
• ISSN: 1615-715X
• DOI: 10.1515/ADVGEOM.2008.030

✦ Synopsis

Abstract

We determine, for all three-dimensional non-unimodular Lie groups equipped with a Lorentzian metric, the set of homogeneous geodesics through a point. Together with the results of [G. Calvaruso, Homogeneous structures on three-dimensional Lorentzian manifolds.J. Geom. Phys.57(2007), 1279–1291. MR2287304 (2008b:53066) Zbl 1112.53051] and [G. Calvaruso, R. A. Marinosci, Homogeneous geodesics of three-dimensional unimodular Lorentzian Lie groups.Mediterr. J. Math.3(2006), 467–481. MR2274738 Zbl pre05151042], this leads to the full classification of three-dimensional Lorentzian g.o. spaces and naturally reductive spaces.