A.V. Podobryaev. One-parametric series of SO(1,1)-symmetric (sub-)Lorentzian structures on the universal covering of SL(2, R) // Journal of Geometry and Physics. 227 (2026) 105875, 12p. DOI: https://doi.org/10.1016/j.geomphys.2026.105875
We consider a one-parametric series of left-invariant Lorentzian structures on the universal covering of the Lie group SL(2, R). These structures have SO(1,1)-symmetry and they are deformations of the anti-de Sitter Lorentzian manifold. We study the global optimality of extremal trajectories, i.e., we describe the longest arcs. The sub-Lorentzian structure appears as a limit case of the considered series of Lorentzian structures. We study how the several properties of the Lorentzian structures deform to the properties of the sub-Lorentzian structure.