Characterizing Of Dual Focal Curves In D

abstract: In this paper, we study dual focal curves in the Dual Lorentzian 3-space D 3 1 . We characterize dual focal curves in terms of their dual focal curvatures

On Dual Curves of DAW(k)-Type and Their Evolutes

In this paper, we study to express the theory of curves including a wide section of Euclidean geometry in terms of dual vector calculus which has an important place in the three -dimensional dual space $\mathbb{D}^{3}$. In other words, we study $DAW(k)$-type curves $\left( 1\leq k\leq 3\right)$ by using Bishop frame defined as alternatively of these curves and give some of their properties in $\mathbb{D}^{3}$. \ Moreover, we define the notion of evolutes of dual spherical curves for ruled surfaces. Finally, we give some examples to illustrate our findings