DIRECTION CURVES OF GENERALIZED BERTRAND CURVES AND INVOLUTE-EVOLUTE CURVES IN E4

In this study, we define (1,3)-Bertrand-direction curve and (1,3)-Bertrand-donor curve in the 4-dimensional Euclidean space E-4. We introduce necessary and sufficient conditions for a special Frenet curve to have a (1,3)-Bertrand-direction curve. We introduce the relations between Frenet vectors and curvatures of these direction curves. Furthermore, we investigate whether (1,3)-evolute-donor curves in E-4 exist and show that there is no (1,3)-evolute-donor curve in E-4.