What question did this study set out to answer?

The aim is to generalize Bertrand curves in Euclidean 3-space and explore their properties.

March 1, 2026

On Generalized Bertrand Curves In Euclidean 3-Space

Key Points

The aim is to generalize Bertrand curves in Euclidean 3-space and explore their properties.
Generalization of Bertrand curve conditions from Minkowski 3-space to Euclidean 3-space.
Analysis of relationships between Frenet vectors and curvature functions.
Construction of an example curve that satisfies the generalized conditions.
New relations between Frenet vectors and curvature functions are established.
An example of a curve fulfilling the generalized Bertrand conditions is provided.

Abstract

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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Cite This Study

Demir et al. (Sun,) studied this question.

synapsesocial.com/papers/69a3d7ccec16d51705d2e18f https://doi.org/https://doi.org/10.22190/fumi221215013d