A new approach to curve couples with Bishop frame

Year 2024, Volume: 73 Issue: 3, 674 - 683, 27.09.2024

Faik Babadağ , Ali Atasoy

https://doi.org/10.31801/cfsuasmas.1329210

Cited By: 1

https://izlik.org/JA97SK94UA

Abstract

This paper presents a detailed study of a new generation of the Bishop frame with components including three orthogonal unit vectors, which are tangent vector, normal vector and binormal vector. It is a frame field described on a curve in Euclidean space, which is an alternative to the Frenet frame. It is useful for curves for which the second derivative is not available. Moreover, the conditions which the Bishop frame of one curve coincides with the Bishop frame of another curve are defined. It would be valuable to replicate similar approaches in the Bishop frame of one curve coincides with the Bishop frame of another curve.

Keywords

Bishop frame , Frenet frame , curvature , regular curve , position vector

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