CHARACTERIZATIONS OF HELICES BY USING THEIR DARBOUX VECTORS

DÜLDÜL M., UYAR DÜLDÜL B.

Sigma Journal of Engineering and Natural Sciences, cilt.38, sa.3, ss.1299-1306, 2020 (ESCI, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 3
  • Basım Tarihi: 2020
  • Dergi Adı: Sigma Journal of Engineering and Natural Sciences
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Directory of Open Access Journals
  • Sayfa Sayıları: ss.1299-1306
  • Anahtar Kelimeler: curvatures, Darboux vector, generalized helix, slant helix
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.