Helix curves of the unit tangent bundle of a pseudo-Riemannian surface
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916605674389504 |
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| author | Abbassi, Mohamed Tahar Kadaoui Boulagouaz, Khadija |
| author_facet | Abbassi, Mohamed Tahar Kadaoui Boulagouaz, Khadija |
| contents | In this paper, we classify helix (spacelike, timelike and null) curves, directed by the geodesic flow vector field, on the (3-dimensional) unit tangent bundle of a pseudo-Riemannian surface of constant Gaussian curvature endowed with a pseudo-Riemannian $g$-natural metric of Kaluza-Klein type. We find, in particular, that every such helix curve is, in fact, a circular helix in the senses that its curvature and torsion are constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Helix curves of the unit tangent bundle of a pseudo-Riemannian surface Abbassi, Mohamed Tahar Kadaoui Boulagouaz, Khadija Differential Geometry 53B25, 53C25, 53C40 In this paper, we classify helix (spacelike, timelike and null) curves, directed by the geodesic flow vector field, on the (3-dimensional) unit tangent bundle of a pseudo-Riemannian surface of constant Gaussian curvature endowed with a pseudo-Riemannian $g$-natural metric of Kaluza-Klein type. We find, in particular, that every such helix curve is, in fact, a circular helix in the senses that its curvature and torsion are constant. |
| title | Helix curves of the unit tangent bundle of a pseudo-Riemannian surface |
| topic | Differential Geometry 53B25, 53C25, 53C40 |
| url | https://arxiv.org/abs/2502.05646 |