The relationship between the Frenet frame and the lightcone frame of a mixed-type curve in Minkowski 3-space

Ergün E.

Optik, vol.274, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 274
  • Publication Date: 2023
  • Doi Number: 10.1016/j.ijleo.2023.170514
  • Journal Name: Optik
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC
  • Keywords: Frenet frame, Lightcone frame, Mixed-type curve
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In the present paper, we give the relationship between the Frenet frame and the lightcone frame of a mixed-type curve. We present the curvature κ and the torsion τ of a mixed-type curve in terms of its lightcone semi-polar coordinates. Finally, the Darboux vector of the curve is expressed as a linear combination of the lightcone frame and the lightcone semi-polar coordinates.