Ruled surfaces and hyper-dual tangent sphere bundle
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909412341317632 |
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| author | Derkaoui, Khadidja Hathout, Fouzi Bekar, Murat Yayli, Yusuf |
| author_facet | Derkaoui, Khadidja Hathout, Fouzi Bekar, Murat Yayli, Yusuf |
| contents | In this study, we define the unit hyper-dual sphere $S_{\mathbb{D} _{2}}$ in hyper-dual vectors $\mathbb{D}_{2}$ and we give E-Study map version in $\mathbb{D}_{2}$ which prove that $S_{\mathbb{D} _{2}}^{2} $ is isomorphism to the tangent bundle $TS_{\mathbb{D} }^{2}.$ Next, we define ruled surfaces in $\mathbb{D}$, we give its developability condition and a geometric interpretation in $\mathbb{R}^{3}$ of any curves in $\mathbb{D}_{2}$. Finally, we present a relationship between a ruled surfaces set in $\mathbb{R}^{3}$ and curves in hyper dual vectors $\mathbb{D}_{2}$. We close each study with examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_01727 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ruled surfaces and hyper-dual tangent sphere bundle Derkaoui, Khadidja Hathout, Fouzi Bekar, Murat Yayli, Yusuf Differential Geometry 53A04, 53A05, 53A17, 55R25 In this study, we define the unit hyper-dual sphere $S_{\mathbb{D} _{2}}$ in hyper-dual vectors $\mathbb{D}_{2}$ and we give E-Study map version in $\mathbb{D}_{2}$ which prove that $S_{\mathbb{D} _{2}}^{2} $ is isomorphism to the tangent bundle $TS_{\mathbb{D} }^{2}.$ Next, we define ruled surfaces in $\mathbb{D}$, we give its developability condition and a geometric interpretation in $\mathbb{R}^{3}$ of any curves in $\mathbb{D}_{2}$. Finally, we present a relationship between a ruled surfaces set in $\mathbb{R}^{3}$ and curves in hyper dual vectors $\mathbb{D}_{2}$. We close each study with examples. |
| title | Ruled surfaces and hyper-dual tangent sphere bundle |
| topic | Differential Geometry 53A04, 53A05, 53A17, 55R25 |
| url | https://arxiv.org/abs/2412.01727 |