Abstract
In this paper we give a new definition of harmonic curvature functions in terms of B 2 and we define a new kind of slant helix which we call quaternionic B 2–slant helix in 4–dimensional Euclidean space E 4 by using the new harmonic curvature functions. Also we define a vector field D which we call Darboux quaternion of the real quaternionic B 2–slant helix in 4–dimensional Euclidean space E 4 and we give a new characterization such as: \({``\alpha : I \subset {\mathbb R} \rightarrow E^4}\) is a quaternionic B 2–slant helix \({\Leftrightarrow H^\prime_2 -KH_{1} = 0"}\) where H 2, H 1 are harmonic curvature functions and K is the principal curvature function of the curve α.
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Gök, İ., Okuyucu, O.Z., Kahraman, F. et al. On the Quaternionic B 2-Slant Helices in the Euclidean Space E 4 . Adv. Appl. Clifford Algebras 21, 707–719 (2011). https://doi.org/10.1007/s00006-011-0284-6
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DOI: https://doi.org/10.1007/s00006-011-0284-6