Direction curves of generalized Bertrand curves and involute-evolute curves in $E^{4}$

Year 2022, , 326 - 338, 30.06.2022

Mehmet Önder

https://doi.org/10.31801/cfsuasmas.950707

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 $E^{4}$ .

Keywords

Direction curve, (1,3)-Bertrand-direction curve, (0,2)-involute-direction curve

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