Biconservative Surfaces in Robertson-Walker Spaces
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909302105571328 |
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| author | Turgay, Nurettin Cenk Şen, Rüya Yeğin |
| author_facet | Turgay, Nurettin Cenk Şen, Rüya Yeğin |
| contents | In this paper, we mainly focus on space-like PMCV surfaces in Robertson-Walker spacetimes. First, we derive certain geometrical properties of biconservative surfaces in the Robertson-Walker space $L^n_1(f, c)$ of arbitrary dimension. Then, we get complete local classifications of such surfaces in $L^4_1(f,0)$, $L^5_1(f,0)$ and $L^5_1(1,\pm 1)$. Finally, we proved that a space-like PMCV biconservative surface in $L^n_1(f,0)$ lies on a totally geodesic submanifold with dimension $4$ or $5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00132 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Biconservative Surfaces in Robertson-Walker Spaces Turgay, Nurettin Cenk Şen, Rüya Yeğin Differential Geometry 53A10(Primary), 53C42 In this paper, we mainly focus on space-like PMCV surfaces in Robertson-Walker spacetimes. First, we derive certain geometrical properties of biconservative surfaces in the Robertson-Walker space $L^n_1(f, c)$ of arbitrary dimension. Then, we get complete local classifications of such surfaces in $L^4_1(f,0)$, $L^5_1(f,0)$ and $L^5_1(1,\pm 1)$. Finally, we proved that a space-like PMCV biconservative surface in $L^n_1(f,0)$ lies on a totally geodesic submanifold with dimension $4$ or $5$. |
| title | Biconservative Surfaces in Robertson-Walker Spaces |
| topic | Differential Geometry 53A10(Primary), 53C42 |
| url | https://arxiv.org/abs/2409.00132 |