Strictly abnormal geodesics with a degeneracy point in the interior of their domain
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916740064083968 |
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| author | Paddeu, Nicola Socionovo, Alessandro |
| author_facet | Paddeu, Nicola Socionovo, Alessandro |
| contents | In this article, we study abnormal curves in a family of sub-Riemannian manifolds of rank 2. We focus on abnormal curves whose lifts to the cotangent bundle annihilate, at an interior point of the domain, all Lie brackets of length up to three of vector fields tangent to the distribution. We present a method to prove that such curves are length-minimizing. Finally, we prove that strictly abnormal geodesics may cease to be locally length-minimizing after a change of the metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11284 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strictly abnormal geodesics with a degeneracy point in the interior of their domain Paddeu, Nicola Socionovo, Alessandro Differential Geometry Optimization and Control 53C17 In this article, we study abnormal curves in a family of sub-Riemannian manifolds of rank 2. We focus on abnormal curves whose lifts to the cotangent bundle annihilate, at an interior point of the domain, all Lie brackets of length up to three of vector fields tangent to the distribution. We present a method to prove that such curves are length-minimizing. Finally, we prove that strictly abnormal geodesics may cease to be locally length-minimizing after a change of the metric. |
| title | Strictly abnormal geodesics with a degeneracy point in the interior of their domain |
| topic | Differential Geometry Optimization and Control 53C17 |
| url | https://arxiv.org/abs/2505.11284 |