One-parametric series of SO(1,1)-symmetric (sub-)Lorentzian structures on the universal covering of SL(2,R)
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914578809487360 |
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| author | Podobryaev, A. V. |
| author_facet | Podobryaev, A. V. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_07259 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | One-parametric series of SO(1,1)-symmetric (sub-)Lorentzian structures on the universal covering of SL(2,R) Podobryaev, A. V. Differential Geometry Optimization and Control 53C50, 53C30, 49J15 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. |
| title | One-parametric series of SO(1,1)-symmetric (sub-)Lorentzian structures on the universal covering of SL(2,R) |
| topic | Differential Geometry Optimization and Control 53C50, 53C30, 49J15 |
| url | https://arxiv.org/abs/2603.07259 |