On the quaternionic Bertrand curves of AW k -type in Euclidean space E³

Year 2019, Volume: 2 Issue: 3, 1 - 11, 01.10.2019

Sezai Kızıltuğ Gökhan Mumcu

Abstract

In this paper, We consider that the curvature conditions of AW k -type 1 ≤k≤ 3 quaternioniccurves in Euclidean space E3and investigates quaternionic Bertrand curves α : I → Q with k 6= 0and r 6= 0. Besides, we show that quaternionic Bertrand curves to be AW 2 -type and AW 3 -typequaternionic curves in E. But it is shown that there is no such a quaternionic Bertrand curve ofAW 1 -type

Keywords

AW k -type curve, General helix, Bertrand curves, Euclidean space, Quaternion algebra

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