Sub-Lorentzian extremals defined by an antinorm
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916289309573120 |
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| author | Podobryaev, A. V. |
| author_facet | Podobryaev, A. V. |
| contents | We consider a left-invariant (sub-)Lorentzian structure on a Lie group. We assume that this structure is defined by a closed convex salient cone in the corresponding Lie algebra and a continuous antinorm associated with this cone. We derive the Hamiltonian system for (sub-)Lorentzian extremals and give conditions under that normal extremal trajectories keep their causal type. Tangent vectors of abnormal extremal trajectories are either light-like or tangent vectors of sub-Riemannian extremal trajectories for the sub-Riemannian distribution spanned by the cone. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04687 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sub-Lorentzian extremals defined by an antinorm Podobryaev, A. V. Optimization and Control Differential Geometry 53C50, 53C30, 49J15 We consider a left-invariant (sub-)Lorentzian structure on a Lie group. We assume that this structure is defined by a closed convex salient cone in the corresponding Lie algebra and a continuous antinorm associated with this cone. We derive the Hamiltonian system for (sub-)Lorentzian extremals and give conditions under that normal extremal trajectories keep their causal type. Tangent vectors of abnormal extremal trajectories are either light-like or tangent vectors of sub-Riemannian extremal trajectories for the sub-Riemannian distribution spanned by the cone. |
| title | Sub-Lorentzian extremals defined by an antinorm |
| topic | Optimization and Control Differential Geometry 53C50, 53C30, 49J15 |
| url | https://arxiv.org/abs/2402.04687 |