Maximal graph surfaces on four-dimensional two-step sub-Lorentzian structures (Q530278)

Sub-Lorentzian geometry is a generalization of Minkowski geometry. In previous works, classes of sub-Lorentzian structures were described, their geodesics were studied and some global properties were obtained. In particular, sub-Lorentzian structures on H-type groups have applications in physics, as geodesics are related with the motion of a relativistic particle in the electromagnetic field. In the present paper, four-dimensional sub-Lorentzian structures are studied and classes of maximal graph surfaces on them are described. Maximality conditions in terms of the Lorentzian mean curvature are derived.