Area formula for graph surfaces on five-dimensional sub-Lorentzian structures (Q2631213)

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, properties of graph mappings with values in a five-dimensional sub-Lorentzian structure are studied. In particular, cases where the graph surface has codimension two or there are two negative directions in the sub-Lorentzian structure are investigated. The area formula for these graph surfaces is obtained.