A new approach to Bertrand curves in Euclidean 3-space

CAMCI Ç., Uçum A., İlarslan K.

Journal of Geometry, vol.111, no.3, 2020 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 111 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.1007/s00022-020-00560-5
  • Journal Name: Journal of Geometry
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Keywords: Anti-Salkowski curves, Bertrand curves, Euclidean 3-space, General helices
  • Çanakkale Onsekiz Mart University Affiliated: Yes

Abstract

In this article, a new approach is given for Bertrand curves in 3-dimensional Euclidean space. According to this approach, the necessary and sufficient conditions including the known results have been obtained for a curve to be Bertrand curve in E3. In addition, the related examples and graphs are given by showing that general helices and anti-Salkowski curves can be Bertrand curves or their mates, which is their new characterization.