Direction curves of generalized Bertrand curves and involute-evolute curves in E 4
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Date
2022
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Publisher
Ankara Üniversitesi
Abstract
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
.
Description
Keywords
Direction curve, (1,3)-Bertrand-direction curve, (0,2)-involute-direction curve