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

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.

On (contra)pedals and (anti)orthotomics of frontals in de Sitter 2‐space

“…Several interesting applications of pedal coordinates in many physical phenomena have been demonstrated in recent papers [2–4]. In addition, some other recent papers about the geometry of pedal curves are [5–9].…”

Framed Natural Mates of Framed Curves in Euclidean 3-Space

“…Moreover, Legendre curves are a special case of framed curves. Therefore, References [52][53][54][55][56][57][58][59][60][61][62][63][64][65] are other notable studies that contribute to the field of framed curves, specifically in the category of frontal or front curves.…”

Pedal Curves of Non-Lightlike Curves in Minkowski 3-Space

“…Since Minkowski space was proposed, it has been studied by researchers domestically (cf. [13][14][15][16][17]). Bakurová introduced pedal curves in Minkowski plane in [18].…”