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

SEZAİ KIZILTUĞ

Published Online : 25 Dec 2019

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Abstract

In this paper, We consider that the curvature conditions of AW(k)-type (1≤k≤3) quaternionic curves in Euclidean space E³ and investigates quaternionic Bertrand curves α : I→Q with k≠0 and r≠0. Besides, we show that quaternionic Bertrand curves to be AW(2)-type and AW(3)-type quaternionic curves in E³. But it is shown that there is no such a quaternionic Bertrand curve of AW(1)-type.

Keywords : AW(k)-type curve, General helix, Bertrand curves, Euclidean space, Quaternion algebra.

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