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

Authors : Mehmet ÖNDER

Pages : 326-338

Doi:10.31801/cfsuasmas.950707

View : 11 | Download : 6

Publication Date : 2022-06-30

Article Type : Research Paper

Abstract :In this study, we define insert ignore into journalissuearticles values(1,3);-Bertrand-direction curve and insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(1,3);-Bertrand-direction curve. We introduce the relations between Frenet vectors and curvatures of these direction curves. Furthermore, we investigate whether insert ignore into journalissuearticles values(1,3);-evolute-donor curves in $E^{4}$ exist and show that there is no insert ignore into journalissuearticles values(1,3);-evolute-donor curve in $E^{4}$ .
Keywords : Direction curve 1, 3, Bertrand direction curve 0, 2, involute direction curve