Investigation of ruled surfaces via Frenet frame in 2-dimensional light cone

Journal: Region - Educational Research and Reviews DOI: 10.32629/rerr.v7i5.4064

Jiangxiang GAO

Department of Mathematics, Kunsan National University

Abstract

This paper focuses on the developability, minimality and curvature characteristics of ruled surfaces in 2-dimensional light cone Q2. First, we review the basic curve theory of Q2. And then, we give the equation of ruled surfaces in Q2 via Fernet frame and calculate the Gaussian and mean curvature of this ruled surface. Finally, we analyze the condition for developable and minimal ruled surfaces in Q2.

Keywords

Frenet frame; light cone; ruled surface

References

[1]Liu HL. 2004. Curves in the light cone. Beitr Algebra Geom, 45(1): 291-303.
https://doi.org/10.1002/cpa.316045080.
[2] Ali U. 2021. Ruled surfaces obtained by curves in the light cone. General Mathematics, 29(1): 55-61.
[3] Barrett ON. 1983. Semi-Riemannian Geometry with Applications to Relativity. Academic Press: Mew York, NY, USA.

Copyright © 2025 Jiangxiang GAO

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License