Investigation of ruled surfaces via Frenet frame in 2-dimensional light cone
Journal: Region - Educational Research and Reviews DOI: 10.32629/rerr.v7i5.4064
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
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[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.
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.
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