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

Kaixin Yao,Donghe Pei,Meixuan Li,Pengcheng Li

doi:10.3390/sym14010059

Abstract

We study the notions of pedal curves, contrapedal curves and B-Gauss maps of non-lightlike regular curves in Minkowski 3-space. Then we establish the relationships among the evolutes, the pedal and contrapedal curves. Moreover, we also investigate the singularities of these objects. Finally, we show some examples to comprehend the characteristics of the pedal and contrapedal curves in Minkowski 3-space.

Highlights

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In [20], when the base curves have singularities, the pedal curves are defined by Li and Pei. They investigated its singularity and calculated the relationships between the singular point of the pedal curves and inflection point. Another important study was done by Izumiya, Pei and Sano in [5], they gave the notions of the lightcone pedal curves and lightcone Gauss map
They established the relationships among singularities of these objects. They proved that there is a correspondence between the singularity of the pedal curve and the lightcone Gauss map

Summary

Introduction

They investigated its singularity and calculated the relationships between the singular point of the pedal curves and inflection point Another important study was done by Izumiya, Pei and Sano in [5], they gave the notions of the lightcone pedal curves and lightcone Gauss map. They established the relationships among singularities of these objects. They proved that there is a correspondence between the singularity of the pedal curve and the lightcone Gauss map.

Preliminaries

Non-Lightlike Pedal Cueves in R31

Singularities of 3-Dimensional Non-Lightlike Curves

Examples