In this paper, we investigate the representation of curves on the lightlike cone ℚ³₂ in Minkowski space ℝ⁴₂ by structure functions. In addition, with this representation, we classify all of the null curves on the lightlike cone ℚ³₂ in four types, and we obtain a natural Frenet frame for these null curves. Furthermore, for this natural Frenet frame, we calculate curvature functions of a null curve, especially the curvature function κ₂ = 0 , and we show that any null curve on the lightlike cone is a helix. Finally, we find all curves with constant curvature functions.
N. Abazari et al., "A Natural Frenet Frame for Null Curves on the Lightlike Cone in Minkowski Space ℝ⁴₂," Journal of Inequalities and Applications, vol. 2020, no. 1, SpringerOpen, Nov 2020.
The definitive version is available at https://doi.org/10.1186/s13660-020-02500-y
Mathematics and Statistics
Keywords and Phrases
Constant curvature function; Helix; Lightlike cone; Natural Frenet frame; Null curve
International Standard Serial Number (ISSN)
Article - Journal
© 2021 The Authors, All rights reserved.
01 Nov 2020