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| Natura: | Preprint |
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2024
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| Accesso online: | https://arxiv.org/abs/2409.11050 |
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| _version_ | 1866910607324741632 |
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| author | Demirci, Burcu Bektaş Turgay, Nurettin Cenk |
| author_facet | Demirci, Burcu Bektaş Turgay, Nurettin Cenk |
| contents | In this article, we study space-like and time-like surfaces in a Robertson-Walker space-time,, denoted by $L^4_1(f,c)$, having positive relative nullity. First, we give the necessary and sufficient conditions for such space-like and time-like surfaces in $L^4_1(f,c)$. Then, we obtain the local classification theorems for space-like and time-like surfaces in $L^4_1(f,0)$ with positive relative nullity. Finally, we consider the space-like and time-like surfaces in $\mathbb{E}^1_1\times\mathbb{S}^3$ and $\mathbb{E}^1_1\times\mathbb{H}^3$ with positive relative nullity. These are the special spaces of $L^4_1(f,c)$ when the warping function $f$ is a constant function, with $c=1$ for $\mathbb{E}^1_1\times\mathbb{S}^3$ and $c=-1$ for $\mathbb{E}^1_1\times\mathbb{H}^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11050 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Surfaces in Robertson-Walker Space-Times with Positive Relative Nullity Demirci, Burcu Bektaş Turgay, Nurettin Cenk Differential Geometry 53C42 In this article, we study space-like and time-like surfaces in a Robertson-Walker space-time,, denoted by $L^4_1(f,c)$, having positive relative nullity. First, we give the necessary and sufficient conditions for such space-like and time-like surfaces in $L^4_1(f,c)$. Then, we obtain the local classification theorems for space-like and time-like surfaces in $L^4_1(f,0)$ with positive relative nullity. Finally, we consider the space-like and time-like surfaces in $\mathbb{E}^1_1\times\mathbb{S}^3$ and $\mathbb{E}^1_1\times\mathbb{H}^3$ with positive relative nullity. These are the special spaces of $L^4_1(f,c)$ when the warping function $f$ is a constant function, with $c=1$ for $\mathbb{E}^1_1\times\mathbb{S}^3$ and $c=-1$ for $\mathbb{E}^1_1\times\mathbb{H}^3$. |
| title | Surfaces in Robertson-Walker Space-Times with Positive Relative Nullity |
| topic | Differential Geometry 53C42 |
| url | https://arxiv.org/abs/2409.11050 |