
handle: 20.500.14002/7602
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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