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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.21065 |
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| _version_ | 1866909925571035136 |
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| author | Catalá, Daniella Vollmayr-Lee, Miriam Bravo-Doddoli, Alejandro |
| author_facet | Catalá, Daniella Vollmayr-Lee, Miriam Bravo-Doddoli, Alejandro |
| contents | This paper investigates sub-Riemannian geodesics within the jet space of curves. We establish the existence of two distinct families of metric lines, that is, globally minimizing geodesics, in the $2$-jet space of plane curves. This result provides an initial contribution toward the broader classification of metric lines in jet spaces. Additionally, we present precise criteria, which characterize when a sub-Riemannian geodesic in the $2$-jet space of plane curves can be identified as a metric line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21065 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Metric Lines in the Space of Curves Catalá, Daniella Vollmayr-Lee, Miriam Bravo-Doddoli, Alejandro Differential Geometry This paper investigates sub-Riemannian geodesics within the jet space of curves. We establish the existence of two distinct families of metric lines, that is, globally minimizing geodesics, in the $2$-jet space of plane curves. This result provides an initial contribution toward the broader classification of metric lines in jet spaces. Additionally, we present precise criteria, which characterize when a sub-Riemannian geodesic in the $2$-jet space of plane curves can be identified as a metric line. |
| title | Metric Lines in the Space of Curves |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2511.21065 |