On Time-Like Class $\mathcal A$ Surfaces in a Static Space Time
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_ | 1866908548972150784 |
|---|---|
| author | Kaya, Furkan Turgay, Nurettin Cenk |
| author_facet | Kaya, Furkan Turgay, Nurettin Cenk |
| contents | In this paper, we consider time-like surfaces in the static space-time given by the warped product $\mathbb L^3_1(c)\, _f\times (I,dz^2)$, where $\mathbb L^3_1(c)$ denotes the Lorentzian space form with the constant sectional curvature $c\in\{-1,0,1\}$. In particular, we study the surfaces with light-like $\left(\frac{\partial}{\partial z}\right)^T$. First, we construct a globally defined pseudo-orthonormal frame field on a surface satisfying this condition and deal with the invariants associated with this frame field. Then, we obtain a complete classification theorem for class~$\mathcal A$ surfaces. Finally, we consider some applications of this theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16220 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Time-Like Class $\mathcal A$ Surfaces in a Static Space Time Kaya, Furkan Turgay, Nurettin Cenk Differential Geometry 53C42 (Primary), 53A10 In this paper, we consider time-like surfaces in the static space-time given by the warped product $\mathbb L^3_1(c)\, _f\times (I,dz^2)$, where $\mathbb L^3_1(c)$ denotes the Lorentzian space form with the constant sectional curvature $c\in\{-1,0,1\}$. In particular, we study the surfaces with light-like $\left(\frac{\partial}{\partial z}\right)^T$. First, we construct a globally defined pseudo-orthonormal frame field on a surface satisfying this condition and deal with the invariants associated with this frame field. Then, we obtain a complete classification theorem for class~$\mathcal A$ surfaces. Finally, we consider some applications of this theorem. |
| title | On Time-Like Class $\mathcal A$ Surfaces in a Static Space Time |
| topic | Differential Geometry 53C42 (Primary), 53A10 |
| url | https://arxiv.org/abs/2509.16220 |