Evolutoids and Pedaloids of Minkowski Plane Curves

AYDIN ŞEKERCİ G., Izumiya S.

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, vol.44, no.5, pp.2813-2834, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 5
  • Publication Date: 2021
  • Doi Number: 10.1007/s40840-021-01091-1
  • Journal Name: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.2813-2834
  • Keywords: Minkowski plane curve, Pedaloids, Evolutoids, Frontal
  • Süleyman Demirel University Affiliated: Yes

Abstract

We consider evolutoids and pedaloids of curves and frontals in the Minkowski plane. Firstly, we present the families of curves by using the pedals and evolutes of regular curves. We investigate the relationships between these families of curves, which are called evolutoids and pedaloids. Also, defining the notion of contrapedaloids, we investigate the similarity in relationships for them. Then, we generalize these notions to frontals by using their moving frame since the evolutoid or pedaloid is not defined as classical way for curves with singular points. Finally, we give examples that confirm our results.