Work

Coinciding Bishop frames and the geometry of W-Bertrand curves

Year: 2025

Type: article

Abstract: Three orthogonal unit vectors—the tangent, normal, and binormal vectors—are among the components of a new generation of the Bishop frame that are thoroughly examined in this research. An alternative to the Frenet frame, it is a frame field specified on a curve in Euclidean space. For curves for which the second derivative is unavailable, it is helpful. In addition, the circumstances under which the Bishop frame of one curve and the Bishop frame of another coincide are specified. Replicating such strategies when the Bishop frame of one curve coincides with the Bishop frame of another curve would be beneficial. In our article, we will present the concept of W-Bertrand curves according to the Bishop frame in the Euclidean $ 3 $-space and examine several kinds of W-Bertrand curves based on the Bishop frame.

Source: AIMS Mathematics

DOI: 10.3934/math.2025807

Authors: Mervat Elzawy, Safaa Mosa

Institutions: Tanta University, Taibah University, Damanhour University, University of Bisha

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

OpenAlex ID: W4413207757