Homogeneous Geodesics of Three-Dimensional Unimodular Lorentzian Lie Groups

We consider three-dimensional unimodular Lie groups equipped with a Lorentzian metric and we determine, for all of them, their sets of homogeneous geodesics through a point. Dedicated to the memory of Professor Aldo Cossu Authors supported by funds of M.U.R.S.T., G.N.S.A.G.A. and the University of Lecce.