Associated curves of a Frenet curve and their applications

摘要

We introduce the notion of the principal (binormal)-direction curve and principal (binormal)-donor curve of a Frenet curve in E3 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.