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 $TS{\mathbb{D} }^{2}.$ 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.