A note on helices in the Euclidean space and in the hyperbolic space
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913945826099200 |
|---|---|
| author | López, Rafael |
| author_facet | López, Rafael |
| contents | We prove that general helices in Euclidean space for Killing vector fields associated to rotations are helices, that is, curves with constant curvature and constant torsion. In hyperbolic space $\h^3$, we obtain the parametrization of helices for the Killing vector fields associated to hyperbolic rotations, spherical rotations and parabolic rotations. It is proved that these helices are geodesics in suitable surfaces of $\h^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12861 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on helices in the Euclidean space and in the hyperbolic space López, Rafael Differential Geometry 53A04, 53B25 We prove that general helices in Euclidean space for Killing vector fields associated to rotations are helices, that is, curves with constant curvature and constant torsion. In hyperbolic space $\h^3$, we obtain the parametrization of helices for the Killing vector fields associated to hyperbolic rotations, spherical rotations and parabolic rotations. It is proved that these helices are geodesics in suitable surfaces of $\h^3$. |
| title | A note on helices in the Euclidean space and in the hyperbolic space |
| topic | Differential Geometry 53A04, 53B25 |
| url | https://arxiv.org/abs/2507.12861 |