Abstract
In this paper, we consider the pedal curves of the mixed-type curves in the Lorentz–Minkowski plane R12. 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.
Highlights
We considered the evolutoids of mixed-type curves in R21
Li and the second author of this paper studied the pedal curve of the given curves with singular points in R2
Is a lightlike point, it is probably not always possible to define a pedal curve of a mixed type curve
Summary
Curves of the Mixed-Type Curves in the Lorentz-Minkowski Plane. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Curves in Lorentz space do not always consist of a single type of points, but rather can involve all three types of points. Liu and the second author of this paper gave the lightcone frame in Lorentz 3-space and considered mixed-type curves in this space. Li and the second author of this paper studied the pedal curve of the given curves with singular points in R2. On the topic of pedal curves of mixed-type curves in R21 , which is an interesting and worthy subject, there have not been relevant investigations. We consider when the pedal curves of mixed-type curves have singular points and investigate the relationship of the types of points of the pedal curves and the base curves. All maps and manifolds in this paper are infinitely differentiable
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