A New Description of Q-Helices in Euclidean 4-Space

Ünal D., Ünlütürk Y., EKİCİ C.

Differential Equations and Dynamical Systems, 2025 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2025
  • Doi Number: 10.1007/s12591-025-00713-5
  • Journal Name: Differential Equations and Dynamical Systems
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
  • Keywords: Four-dimensional Euclidean space E4, q-frame, q-helices, The associations among q-helices
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

In this study, slant helices are investigated via quasi-frame (abbv. q-frame) in four-dimensional Euclidean space E4. The notion of k-type slant q-helices is introduced in E4. Each of the q-frame fields T,Nq,Bq,Cq which makes constant angles with a non-zero fixed axis is surveyed one by one. Also, the conditions for each type of q-helices are obtained and their associations to each other are analyzed in detail.