Existence of the longest arcs for left-invariant three-dimensional contact sub-Lorentzian structures
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912951613521920 |
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| author | Podobryaev, A. V. |
| author_facet | Podobryaev, A. V. |
| contents | The problem of finding optimal curves (the longest arcs) for sub-Lorentzian structures is an optimal control problem with an unbounded control set and a concave cost functional. The question of existence of an optimal solution is nontrivial for such problems. We solve here this question for some left-invariant three-dimensional contact sub-Lorentzian structures, whose classification is known. We propose sufficient conditions for the existence of the longest arcs for left-invariant (sub-)Lorentzian structures on solvable Lie groups and on the universal cover of the Lie group SL(2, R). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07262 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence of the longest arcs for left-invariant three-dimensional contact sub-Lorentzian structures Podobryaev, A. V. Differential Geometry Metric Geometry Optimization and Control 49J15, 53C50, 53C30 The problem of finding optimal curves (the longest arcs) for sub-Lorentzian structures is an optimal control problem with an unbounded control set and a concave cost functional. The question of existence of an optimal solution is nontrivial for such problems. We solve here this question for some left-invariant three-dimensional contact sub-Lorentzian structures, whose classification is known. We propose sufficient conditions for the existence of the longest arcs for left-invariant (sub-)Lorentzian structures on solvable Lie groups and on the universal cover of the Lie group SL(2, R). |
| title | Existence of the longest arcs for left-invariant three-dimensional contact sub-Lorentzian structures |
| topic | Differential Geometry Metric Geometry Optimization and Control 49J15, 53C50, 53C30 |
| url | https://arxiv.org/abs/2603.07262 |