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arXiv · 2603.07259

One-parametric series of SO(1,1)-symmetric (sub-)Lorentzian structures on the universal covering of SL(2,R)

A. V. Podobryaev
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Abstract

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.

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A. V. Podobryaev. 2026-03-07. One-parametric series of SO(1,1)-symmetric (sub-)Lorentzian structures on the universal covering of SL(2,R). https://doi.org/10.1016/j.geomphys.2026.105875

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