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Quaternionic Framed Bertrand Curves

Authors: Azak, Ayşe Zeynep; Sürekçi, Arzu Cihan; Güngör, Mehmet Ali; Sürekçi, Arzu Cihan; BÖLÜMÜ, BİLİŞİM TEKNOLOJİLERİ MESLEK YÜKSEKOKULU/ELEKTRONİK VE OTOMASYON;

Quaternionic Framed Bertrand Curves

Abstract

There is no pair of Bertrand quaternionic curves in the classical sense in quaternionic space. Therefore, realizing that investigating singular points and analyzing their properties and behavior is a rising topic in differential geometry, framed Bertrand mates, which are singular have been defined in the quaternionic space. The characteristic properties of these curves have been given. Thus, we have proven that the distance between these pairs of curves remains constant. The conditions for framed quaternionic curves to be Bertrand mates have been shown. Then, we demonstrate that Bertrand’s partner of any framed quaternionic curve is a framed quaternionic curve. Furthermore, the relationship between the curvatures of quaternionic framed Bertrand curves has been given. Finally, an example has been given that supports the proven theorem in our study. © 2025 Elsevier B.V., All rights reserved.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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