International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

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

  • H. S. Abdel-Aziz1
  • M. Khalifa Saad2*
  • S. A. Mohamed1
  1. Sohag University
  2. Mathematics Department, Faculty of Science, Sohag University

* Corresponding author

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.

How to Cite

H. S. Abdel-Aziz, M. K. Saad, S. A. Mohamed, On Dual Curves of DAW(k)-Type and Their Evolutes, Int. J. Anal. Appl. 16 (2018), 614–627. https://doi.org/10.28924/2291-8639-16-2018-614

BibTeX
@article{Abdel-Aziz2018,
  author  = {Abdel-Aziz, H. S. and Saad, M. Khalifa and Mohamed, S. A.},
  title   = {On Dual Curves of DAW(k)-Type and Their Evolutes},
  journal = {Int. J. Anal. Appl.},
  volume  = {16},
  year    = {2018},
  pages   = {614--627},
  doi     = {10.28924/2291-8639-16-2018-614}
}

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