Existence theorem for sub-Lorentzian problems
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913347573645312 |
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| author | Lokutsievskiy, L. V. Podobryaev, A. V. |
| author_facet | Lokutsievskiy, L. V. Podobryaev, A. V. |
| contents | In this paper, we prove the existence theorem for longest paths in sub-Lorentzian problems, which generalizes the classical theorem for globally hyperbolic Lorentzian manifolds. We specifically address the case of invariant structures on homogeneous spaces, as the conditions for the existence theorem in this case can be significantly simplified. In particular, it turns out that longest paths exist for any left-invariant sub-Lorentzian structures on Carnot groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07975 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence theorem for sub-Lorentzian problems Lokutsievskiy, L. V. Podobryaev, A. V. Differential Geometry Metric Geometry Optimization and Control 49J15, 53C50, 53C30 In this paper, we prove the existence theorem for longest paths in sub-Lorentzian problems, which generalizes the classical theorem for globally hyperbolic Lorentzian manifolds. We specifically address the case of invariant structures on homogeneous spaces, as the conditions for the existence theorem in this case can be significantly simplified. In particular, it turns out that longest paths exist for any left-invariant sub-Lorentzian structures on Carnot groups. |
| title | Existence theorem for sub-Lorentzian problems |
| topic | Differential Geometry Metric Geometry Optimization and Control 49J15, 53C50, 53C30 |
| url | https://arxiv.org/abs/2401.07975 |