Vn-slant helices in Euclidean n-space En

In this paper, we give a definition of harmonic curvature functions in terms of V-n and we define a new kind of a slant helix. We call this new slant helix a V-n-slant helix in n-dimensional Euclidean space En and define it by using new harmonic curvature functions. We also de fine a vector field D which we call a Darboux vector field of a Vn-slant helix in n-dimensional Euclidean space En and we give a new characterization as: alpha : I subset of R -> E-n is a V-n-slant helix <-> Hn-2*' - k1H(n-3)* = 0, where Hn-2*, Hn-3* are harmonic curvature functions and k(1) shows the first curvature function of the curve alpha.