Rotational Weingarten surfaces in Lorentz-Minkowski space
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912757557755904 |
|---|---|
| author | Carretero, Paula Castro, Ildefonso Castro-Infantes, Ildefonso |
| author_facet | Carretero, Paula Castro, Ildefonso Castro-Infantes, Ildefonso |
| contents | We propose a new approach to the study of rotational surfaces in Lorentz-Minkowski space based on the notion of the geometric linear momentum of the generatrix curves with respect to the axes of revolution. This technique allows us to reduce any Weingarten condition on the surface to a first-order ordinary differential equation for the momentum as a function of the distance to the corresponding axis, providing a unified framework that encompasses the three causal types of rotation axes. As a direct application, we classify important families of rotational Weingarten surfaces in this setting, including some linear and quadratic cases. Furthermore, we introduce the non-degenerate quadric surfaces of revolution in Lorentz-Minkowski space and characterize them in terms of a specific cubic Weingarten relation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10423 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rotational Weingarten surfaces in Lorentz-Minkowski space Carretero, Paula Castro, Ildefonso Castro-Infantes, Ildefonso Differential Geometry 53B30, 53A04, 53A05 We propose a new approach to the study of rotational surfaces in Lorentz-Minkowski space based on the notion of the geometric linear momentum of the generatrix curves with respect to the axes of revolution. This technique allows us to reduce any Weingarten condition on the surface to a first-order ordinary differential equation for the momentum as a function of the distance to the corresponding axis, providing a unified framework that encompasses the three causal types of rotation axes. As a direct application, we classify important families of rotational Weingarten surfaces in this setting, including some linear and quadratic cases. Furthermore, we introduce the non-degenerate quadric surfaces of revolution in Lorentz-Minkowski space and characterize them in terms of a specific cubic Weingarten relation. |
| title | Rotational Weingarten surfaces in Lorentz-Minkowski space |
| topic | Differential Geometry 53B30, 53A04, 53A05 |
| url | https://arxiv.org/abs/2512.10423 |