Generalizes Bertrand curves in Euclidean 3-space, revealing curvature relations and providing examples.
In this paper, we generalize the notion of Bertrand curve in Euclidean 3-space analogously as in Minkowski 3-space. According to this generalization, the Bertrand curve conditions of a given space curve are obtained and the relations between Frenet vectors and curvature functions are revealed. A curve that meets the given condition is constructed as an example.
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Demir et al. (2023) studied this question.
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