Bertrand and Mannheim Curves of Spherical Framed Curves in a Three-Dimensional Sphere

Mathematics

Masatomo Takahashi¹  Haiou Yu² 

[1] Muroran Institute of Technology, Muroran 050-8585, Japan;School of Applied Mathematics, Jilin University of Finance and Economic, Changchun 130117, China;

关键词: Bertrand curves;    Mannheim curves;    spherical regular curves;    spherical framed curves;    singularity;   

DOI  :  10.3390/math10081292

来源: DOAJ

【 摘 要 】

We investigated differential geometries of Bertrand curves and Mannheim curves in a three-dimensional sphere. We clarify the conditions for regular spherical curves to become Bertrand and Mannheim curves. Then, we concentrate on Bertrand and Mannheim curves of singular spherical curves. As singular spherical curves, we considered spherical framed curves. We define Bertrand and Mannheim curves of spherical framed curves. We give conditions for spherical framed curves to become Bertrand and Mannheim curves.

【 授权许可】

Unknown