Planar Sub-Lorentzian Problems on the Martine Distribution

The talk investigates two planar (nilpotent) sub-Lorentzian geometry problems on the Martine distribution in 3-dimensional space. For the first problem, the attainable set has a nontrivial intersection with the Martine plane, whereas for the second, it does not. The attainable sets, optimal trajectories, sub-Lorentzian distances, and spheres are described. For the first problem, the sub-Lorentzian sphere is a topological manifold with boundary, while for the second problem, it is an analytic manifold.