Curves According to the Successor Frame in Euclidean 3-Space

Abstract

In the present study, the successor formulae of the successor curves defined by Menninger [1] are given. Then, by defining the successor planes, the geometric meanings of the successor curvatures are investigated and the relations across the components of the position vectors of successor curves are found. Furthermore, in this study, it is proven that lies in the 3rd.type successor plane, lies in the 1st type successor plane and by defining the involute-evolute S-pair, the distance between the corresponding points of these curves is found.