Homogeneous geodesics of three-dimensional unimodular Lorentzian Lie groups (Q879758)

In a previous paper [Commentat. Math. Univ. Carol. 43, 261--270 (2002, Zbl 1090.53038)], \textit{R. A. Marinosci} studied three-dimensional unimodular Lie groups equipped with a left-invariant Riemannian metric. In the paper under review, the authors investigate homogeneous geodesics of three-dimensional unimodular Lie groups admitting a left-invariant Lorentzian metric. The paper is organized as follows. Section 2 is devoted to recall the basic definitions and properties of homogeneous geodesics in a homogeneous pseudo-Riemannian manifold. Section 3 reports the fundamental classification result of three-dimensional unimodular Lorentzian Lie groups and the authors describe the set of geodesic vectors for all these spaces. Finally, in Section 4 there appear the results the authors have found in the different cases about canonical homogeneity and linear independence of homogeneous geodesics.