On the striction curves of involute and bertrandian frenet ruled surfaces in E3

Kiliçoğlu Ş., Şenyurt S., Hilmi Hacisalihoğlu H.

Applied Mathematical Sciences, vol.9, no.141-144, pp.7081-7094, 2015 (Scopus)

  • Publication Type: Article / Article
  • Volume: 9 Issue: 141-144
  • Publication Date: 2015
  • Doi Number: 10.12988/ams.2015.59606
  • Journal Name: Applied Mathematical Sciences
  • Journal Indexes: Scopus
  • Page Numbers: pp.7081-7094
  • Keywords: Bertrand curve pair, Evolute curve, Frenet ruled surface, Involute curve, Ruled surfaces, Striction curves
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

© 2015 Ş. Kiliçoğlu, S. Şenyurt and H. H. Hacisalihoğlu.In this paper, we consider twelve special ruled surfaces associated to the evolute curve α, involute curve α* and Bertrand curve α** with k1 ≠ 0. They are called as Frenet ruled surface, Involute Frenet ruled surfaces, and Bertrandian Frenet ruled surface cause of their generators are the Frenet vector fields of evolute curve α. First we give all the parametriza- tions of all Frenet ruled surfaces. Further we give only three matrices of striction curves along the Frenet ruled surface, Involute Frenet ruled surfaces, and Bertrandian Frenet ruled surface.