Title: On Dual Curves of DAW(k)-Type and Their Evolutes
Author(s): H. S. Abdel-Aziz, M. Khalifa Saad, S. A. Mohamed
Pages: 614-627
Cite as:
H. S. Abdel-Aziz, M. Khalifa Saad, S. A. Mohamed, On Dual Curves of DAW(k)-Type and Their Evolutes, Int. J. Anal. Appl., 16 (5) (2018), 614-627.

Abstract


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.

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