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.
"Extremal Lorentzian surfaces with null $r$-planar geodesics in space forms." Tohoku Math. J. (2) 67 (4) 611 - 634, 2015. https://doi.org/10.2748/tmj/1450798076