2022 # 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.

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2023

2023

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“…Let x = x(s) be a regular unit speed conformable curve in the Euclidean 3−space where s measures its arc length. The following relation exists between the curvature and torsion of the curve x and the conformable curvature and torsion [12]…”

confidence: 99%

“…Let x = x(s) be a regular unit speed conformable curve in the Euclidean 3−space where s measures its arc length. The following relation exists between the curvature and torsion of the curve x and the conformable curvature and torsion [12]…”

confidence: 99%

“…As can be seen from equation ( 2), when x is a unit speed curve, the conformable derivative does not affect the Frenet vectors, so the Frenet vectors do not undergo any change. However, considering equations ( 3) and ( 4), the curvature and torsion of the curve x have changed under the conformable fractional derivative [12].…”

confidence: 99%