On special curves in Lie groups with Myller configuration

İşbilir Z., DOĞAN YAZICI B., Tosun M.

Mathematical Methods in the Applied Sciences, vol.47, no.14, pp.11693-11708, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 14
  • Publication Date: 2024
  • Doi Number: 10.1002/mma.10149
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.11693-11708
  • Keywords: Frenet-type frame, Lie groups, Myller configuration, osculating-type curves, rectifying-type curves, versor field
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

In this study, we determine a new type comprehensive frame, which is called the generalized Frenet-type frame in three-dimensional Lie groups with Myller configurations, and it includes several special and classical type frames for Euclidean 3-space and three-dimensional Lie groups. After constructing this new comprehensive frame, we obtain derivative formulas with the help of the Lie curvature. In addition, we define some special type curves. The geometry of versor fields along a curve with Frenet-type frame in three-dimensional Lie groups with Myller configurations is a generalization of the usual theory of curves. Since this particular relationship, the osculating-type and rectifying-type curves with Frenet-type frame in three-dimensional Lie groups with Myller configurations include some special cases for osculating and rectifying curves in different spaces.