On harmonic curvatures of a Frenet curve

Abstract

In this paper we consider harmonic curvatures of a Frenet curve of osculating order d. We also consider a general helix of AW(k) type where k=l,2 and 3. We have show that, there is no general helix of AW(3)type. We also show that, a general helix of rank 1 and of AW(3) type must be a circular helix. We give curvature conditions of the curves, which have AW(2) property. In the final part, we visualize the plane and space curves of (weak) AW(2)type.