Extremal Lorentzian surfaces with null r-planar geodesics in space forms

We show a congruence theorem for oriented Lorentzian surfaces with horizontal reflector lifts in pseudo-Riemannian space forms of neutral signature. As a corollary, a characterization theorem is obtained for the Lorentzian Boruvka spheres, that is, a full real analytic null r-planar geodesic immersion with vanishing mean curvature vector field is locally congruent to the Lorentzian Boruvka sphere in a $2r$-dimensional space form of neutral signature.