Normal sub-Riemannian geodesics related to filtrations of Lie algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912751193948160 |
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| author | Jovanovic, Bozidar Sukilovic, Tijana Vukmirovic, Srdjan |
| author_facet | Jovanovic, Bozidar Sukilovic, Tijana Vukmirovic, Srdjan |
| contents | There is a natural way to construct sub-Riemannian structures that depend on $n$ parameters on compact Lie groups. These structures are related to the filtrations of Lie subalgebras $\mathfrak g_0 < \mathfrak g_1 < \mathfrak g_2 < \dots < \mathfrak g_{n-1}<\mathfrak g_n=\mathfrak g=Lie(G)$. In the case where $n=1$, the explicit solution for normal sub-Riemannian geodesics was provided by Agrachev, Brockett, and Jurjdevic. We extend their solution to apply to general chains of Lie subgroups. Additionally, we describe normal geodesic lines of the induced sub-Riemannian structures on homogeneous spaces $G/K$, where $\mathfrak g_0=Lie(K)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_05553 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normal sub-Riemannian geodesics related to filtrations of Lie algebras Jovanovic, Bozidar Sukilovic, Tijana Vukmirovic, Srdjan Differential Geometry Optimization and Control Exactly Solvable and Integrable Systems 53C17, 70H06, 70G65, 37J35 There is a natural way to construct sub-Riemannian structures that depend on $n$ parameters on compact Lie groups. These structures are related to the filtrations of Lie subalgebras $\mathfrak g_0 < \mathfrak g_1 < \mathfrak g_2 < \dots < \mathfrak g_{n-1}<\mathfrak g_n=\mathfrak g=Lie(G)$. In the case where $n=1$, the explicit solution for normal sub-Riemannian geodesics was provided by Agrachev, Brockett, and Jurjdevic. We extend their solution to apply to general chains of Lie subgroups. Additionally, we describe normal geodesic lines of the induced sub-Riemannian structures on homogeneous spaces $G/K$, where $\mathfrak g_0=Lie(K)$. |
| title | Normal sub-Riemannian geodesics related to filtrations of Lie algebras |
| topic | Differential Geometry Optimization and Control Exactly Solvable and Integrable Systems 53C17, 70H06, 70G65, 37J35 |
| url | https://arxiv.org/abs/2512.05553 |