On Quaternionic Bertrand Curves in Euclidean $3$-Space

Abstract

In this article, spatial quaternionic Bertrand curve pairs in the 3-dimensional Euclidean space are examined. Algebraic properties of quaternions, basic definitions and theorems are given. Later, some characterizations of spatial quaternionic Bertrand curve pairs are obtained in the 3-dimensional Euclidean space.

Keywords

• Quaternions
• spatial quaternion
• quaternion algebra
• Bertrand curve
• curvatures
• Euclidean space

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