Singularities of lightcone pedals of spacelike curves in Lorentz-Minkowski 3-space

Abstract

Abstract:In this paper, geometric properties of spacelike curves on a timelike surface in Lorentz-Minkowski 3-space are investigated by applying the singularity theory of smooth functions from the contact viewpoint.

Involute–evolute and pedal–contrapedal curve pairs on S2

“…Pedal curves in different space forms are classical topics in the study of geometry. [17][18][19][20] In Li and Pei, 18 pedal curves of spherical Legendre immersion are defined. We will define contrapedal curves of spherical Legendre immersion.…”

“…Pedal curves in different space forms are classical topics in the study of geometry 17‐20 . In Li and Pei, 18 pedal curves of spherical Legendre immersion are defined.…”

“…[5][6][7][8]10,16 Another kind of curves called pedal-contrapedal curves was also studied. [17][18][19][20] However, for spherical curves, the definitions of involutes and contrapedal curves are vague. Motivated by the results of evolutes and pedal curves of spherical curves, we will define involutes and contrapedal curves of spherical curves.…”

“…As a kind of well‐known associated curves, involute–evolute curve pairs in different space forms were studied by many mathematicians 5‐8,10,16 . Another kind of curves called pedal–contrapedal curves was also studied 17‐20 . However, for spherical curves, the definitions of involutes and contrapedal curves are vague.…”