Sub-Lorentzian geometry on the Martinet distribution (Q6634032)

The paper is devoted to two sub-Lorentzian problems on the Martinet distribution and the general goal of the paper is to describe the main features of the solution: optimal synthesis, distance and related spheres. For the first problem, it occurs that the future cone has a nontrivial intersection with the tangent space to the Martinet surface; for the second problem, this intersection is trivial. Accordingly, sub-Lorentzian geometry occurs to be significantly more complicated in the first case. Reachable sets, optimal trajectories, and sub-Lorentzian distances and spheres are described. The article may be of interest to specialists in optimal control theory.