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.
Mathematics Subject Classification (2000). 53C20, 53C22, 53C30.
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 [C] and [CM2], this leads to the full classification of three-dimensional Lorentzian g.o. spaces and naturally reductive spaces.
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