On the Quaternionic B 2-Slant Helices in the Euclidean Space E 4

GÖK İ., OKUYUCU O. Z., Kahraman F., Hacisalihoǧlu H. H.

Advances in Applied Clifford Algebras, vol.21, no.4, pp.707-719, 2011 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 4
  • Publication Date: 2011
  • Doi Number: 10.1007/s00006-011-0284-6
  • Journal Name: Advances in Applied Clifford Algebras
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.707-719
  • Keywords: Euclidean spaces, harmonic curvature functions, quaternion algebra, Slant helices
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

In this paper we give a new definition of harmonic curvature functions in terms of B2 and we define a new kind of slant helix which we call quaternionic B2-slant helix in 4-dimensional Euclidean space E4 by using the new harmonic curvature functions. Also we define a vector field D which we call Darboux quaternion of the real quaternionic B2-slant helix in 4-dimensional Euclidean space E4 and we give a new characterization such as: α:I ⊂ ℝ → E4 isis a quaternionic B2B2-slant helix ↔ H2 -KH1 where H2, H1 are harmonic curvature functions and K is the principal curvature function of the curve α. © 2011 Springer Basel AG.