Associated curves in $E^3$ from a different point of view
AbstractIn this paper, tangent, principal normal and binormal wise associated
curves are defined such that each of these vectors of any given curve
lies on the osculating, normal and rectifying plane of its mate,
respectively. For each associated curves a new moving frame and the
corresponding curvatures are found, and in addition to this the possible
solutions for distance functions between the curve and its associated
mate are discussed. In particular, it is seen that the involute curves
belong to the family of tangent associated curves, the Bertrand and the
Mannheim curves belong to the principal normal associated curves.
Finally, as an application, we present some examples and map a given
curve together with its mate and their frames.