1. Ruled surfaces and hyper-dual tangent sphere bundle
- Author
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Derkaoui, Khadidja, Hathout, Fouzi, Bekar, Murat, and Yayli, Yusuf
- Subjects
Mathematics - Differential Geometry ,53A04, 53A05, 53A17, 55R25 - Abstract
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., Comment: e.g.: 14 pages, 1 figure
- Published
- 2024