Time-like constant slope surfaces and space-like Bertrand curves in Minkowski 3-space
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2012
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| _version_ | 1866914342470942720 |
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| author | Babaarslan, Murat Yayli, Yusuf |
| author_facet | Babaarslan, Murat Yayli, Yusuf |
| contents | Defining Lorentzian Sabban frame of the unit speed time-like curves on de Sitter 2-space $\mathbb{S}^{2}_{1}$ and introducing space-like height function on the unit speed time-like curves on $\mathbb{S}^{2}_{1}$, the invariants of the unit speed time-like curves on $\mathbb{S}^{2}_{1}$ and geometric properties of de Sitter evolutes of the unit speed time-like curves on $\mathbb{S}^{2}_{1}$ are studied. A relation between space-like Bertrand curves and helices is obtained. De Sitter Darboux images of space-like Bertrand curves are equal to de Sitter evolutes. The relations between time-like constant slope surfaces lying in the space-like cone and space-like Bertrand curves in Minkowski 3-space $\mathbb{R}^{3}_{1}$ are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1206_4072 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Time-like constant slope surfaces and space-like Bertrand curves in Minkowski 3-space Babaarslan, Murat Yayli, Yusuf Differential Geometry Defining Lorentzian Sabban frame of the unit speed time-like curves on de Sitter 2-space $\mathbb{S}^{2}_{1}$ and introducing space-like height function on the unit speed time-like curves on $\mathbb{S}^{2}_{1}$, the invariants of the unit speed time-like curves on $\mathbb{S}^{2}_{1}$ and geometric properties of de Sitter evolutes of the unit speed time-like curves on $\mathbb{S}^{2}_{1}$ are studied. A relation between space-like Bertrand curves and helices is obtained. De Sitter Darboux images of space-like Bertrand curves are equal to de Sitter evolutes. The relations between time-like constant slope surfaces lying in the space-like cone and space-like Bertrand curves in Minkowski 3-space $\mathbb{R}^{3}_{1}$ are obtained. |
| title | Time-like constant slope surfaces and space-like Bertrand curves in Minkowski 3-space |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1206.4072 |