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

Abstract

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.