CHARACTERIZATIONS OF HELICES BY USING THEIR DARBOUX VECTORS

DÜLDÜL M., UYAR DÜLDÜL B.

Sigma Journal of Engineering and Natural Sciences, vol.38, no.3, pp.1299-1306, 2020 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 3
  • Publication Date: 2020
  • Journal Name: Sigma Journal of Engineering and Natural Sciences
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Directory of Open Access Journals
  • Page Numbers: pp.1299-1306
  • Keywords: curvatures, Darboux vector, generalized helix, slant helix
  • Yıldız Technical University Affiliated: Yes

Abstract

In this study, firstly, new proofs of the theorems which characterize the generalized helices, slant helices and relatively-normal slant helices are presented by using the Darboux vectors of these helices. Also, a characterization of a generalized helix lying on an oriented surface is given in terms of its geodesic curvature, geodesic torsion and normal curvature. Secondly, by defining B1-slant helix in Euclidean 4-space, we give its characterization.