Maximal simply connected Lorentzian surfaces with a Killing field and their completeness (Q2126087)

In this paper, the author describes simply connected maximal Lorentzian surfaces admitting a complete Killing vector field in terms of the space of Killing orbits and a smooth function defined on it. She studies the completeness of such surfaces and prove in particular that a smooth Lorentzian surface with a complete Killing vector field and bounded curvature is complete if and only if it is null complete. She also provides a completeness criterion involving the topological structure of the space of Killing orbits, or both the topology of this space and the geometry of the surface.