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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.00475 |
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| _version_ | 1866917738606231552 |
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| author | Demirci, Burcu Bektaş Turgay, Nurettin Cenk Şen, Rüya Yeğin |
| author_facet | Demirci, Burcu Bektaş Turgay, Nurettin Cenk Şen, Rüya Yeğin |
| contents | In this article, we consider space-like surfaces in Robertson-Walker Space times $L^4_1(f,c)$ with comoving observer field $\frac{\partial}{\partial t}$. We study some problems related to such surfaces satisfying the geometric conditions imposed on the tangential part and normal part of the unit vector field $\frac{\partial}{\partial t}$ naturally defined. First, we investigate space-like surfaces in $L^4_1(f,c)$ satisfying that the tangent component of $\frac{\partial}{\partial t}$ is an eigenvector of all shape operators, called class $\mathcal A$ surfaces. Then, we get a classification theorem of space-like class $\mathcal A$ surfaces in $L^4_1(f,0)$. Also, we examine minimal space-like class $\mathcal A$ surfaces in $L^4_1(f,0)$. Finally, we give the parametrizations of space-like surfaces in $L^4_1(f,0)$ when the normal part of the unit vector field $\frac{\partial}{\partial t}$ is parallel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00475 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Space-like Class $\mathcal A$ Surfaces in Robertson-Walker Space Times Demirci, Burcu Bektaş Turgay, Nurettin Cenk Şen, Rüya Yeğin Differential Geometry 53C42 In this article, we consider space-like surfaces in Robertson-Walker Space times $L^4_1(f,c)$ with comoving observer field $\frac{\partial}{\partial t}$. We study some problems related to such surfaces satisfying the geometric conditions imposed on the tangential part and normal part of the unit vector field $\frac{\partial}{\partial t}$ naturally defined. First, we investigate space-like surfaces in $L^4_1(f,c)$ satisfying that the tangent component of $\frac{\partial}{\partial t}$ is an eigenvector of all shape operators, called class $\mathcal A$ surfaces. Then, we get a classification theorem of space-like class $\mathcal A$ surfaces in $L^4_1(f,0)$. Also, we examine minimal space-like class $\mathcal A$ surfaces in $L^4_1(f,0)$. Finally, we give the parametrizations of space-like surfaces in $L^4_1(f,0)$ when the normal part of the unit vector field $\frac{\partial}{\partial t}$ is parallel. |
| title | On Space-like Class $\mathcal A$ Surfaces in Robertson-Walker Space Times |
| topic | Differential Geometry 53C42 |
| url | https://arxiv.org/abs/2408.00475 |