Pedal Curves of the Mixed-Type Curves in the Lorentz-Minkowski Plane

Xin Zhao and Donghe Pei
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Xin Zhao: School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
Donghe Pei: School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Mathematics, 2021, vol. 9, issue 22, 1-11

Abstract: In this paper, we consider the pedal curves of the mixed-type curves in the Lorentz–Minkowski plane R 1 2 . The pedal curve is always given by the pseudo-orthogonal projection of a fixed point on the tangent lines of the base curve. For a mixed-type curve, the pedal curve at lightlike points cannot always be defined. Herein, we investigate when the pedal curves of a mixed-type curve can be defined and define the pedal curves of the mixed-type curve using the lightcone frame. Then, we consider when the pedal curves of the mixed-type curve have singular points. We also investigate the relationship of the type of the points on the pedal curves and the type of the points on the base curve.

Keywords: pedal curve; mixed-type curve; lightlike point; Lorentz–Minkowski plane (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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