A New Approach on Type-3 Slant Helix in E^4

In this paper, we introduce type-3 slant helix according to parallel transport frame in 4-dimensional Euclidean Space E^4 and we use a constant angle Ø between a unit and fixed direction vector field X and the last relatively parallel vector field M_3 of the curve, that is, ‹ M_3, X› = cos Ø = const. where ‹,›, is Euclidean inner product. Since the relatively parallel vector field M_3 of the curve makes a constant angle with the unit and fixed direction vector field X we call this curve as a type-3 slant helix in 4-dimensional Euclidean Space E^4. Also we define new harmonic curvature functions and we give a vector field D which we call Darboux vector field for type-3 slant helix. And then we obtain some characterizations for type-3 slant helix in terms of the harmonic curvature functions and the Darboux vector field D.