Flat sub-Lorentzian structures on Martinet distribution

Two flat sub-Lorentzian problems on the Martinet distribution are studied. For the first one, the attainable set has a nontrivial intersection with the Martinet plane, but for the second one it does not. Attainable sets, optimal trajectories, sub-Lorentzian distances and spheres are described. © The authors. Published by EDP Sciences, SMAI 2025.