New moving frames for the curves lying on a surface

Alkan A., Hüseyin K., Ağirman Aydin T.

Sigma Journal of Engineering and Natural Sciences, vol.42, no.4, pp.1023-1029, 2024 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 4
  • Publication Date: 2024
  • Doi Number: 10.14744/sigma.2023.00049
  • 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.1023-1029
  • Keywords: Darboux Frame, Moving Frame, Normal Darboux Vector, Osculator Darboux Vector, Rectifying Darboux Vector
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

In this article, three new orthogonal frames are defined for the curves lying on a surface. These moving frames, obtained based on the Darboux frame, are called “Osculator Darboux Frame”, “Normal Darboux Frame” and “Rectifying Darboux Frame”, respectively. Also, the Osculator Darboux Frame components and curvatures are calculated for a presented example. Cite this article as: Alkan A, Kocayiğit H, Ağırman Aydın T. New moving frames for the curves lying on a surface. Sigma J Eng Nat Sci 2024;42(4):1023−1029.