Ruled surfaces and hyper-dual tangent sphere bundle

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 $T{S}_{\mathbb{D}}^2.$ 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.

e.g.: 14 pages, 1 figure