Constant Ratio Quaternionic Curves in Euclidean Spaces

ÖZTÜRK G., KİŞİ İ., BÜYÜKKÜTÜK S.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, vol.27, no.2, pp.1659-1673, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.1007/s00006-016-0716-4
  • Journal Name: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1659-1673
  • Keywords: Position vectors, Quaternionic curves, Frenet equations
  • Kocaeli University Affiliated: Yes

Abstract

In this paper, we give some characterizations of quaternionic curves whose position vectors can be written as linear combinations of their Serret-Frenet vectors in Euclidean 3-space and Euclidean 4-space . We characterize such curves in terms of their curvature functions. Finally, we give the necessary and sufficient conditions for these types of curves to become constant ratio, T-constant, and N-constant.