Associated curves of a Frenet curve and their applications

We introduce the notion of the principal (binormal)-direction curve and principal (binormal)-donor curve of a Frenet curve in E 3 and give the relationship of curvature and torsion of its mates. As application, we characterize general helices and slant helices in terms of their associated curves and give a canonical method to construct them. Also, we give a new characterization of Bertrand curve.