On the Quaternionic B2-Slant Helices in the Euclidean Space E4

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 of R -> E-4 is a quaternionic B-2-slant helix double left right arrow H-2 - KH1 = 0 where H-2, H-1 are harmonic curvature functions and K is the principal curvature function of the curve alpha.