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

Author

Listed:
  • Masatomo Takahashi

    (Muroran Institute of Technology, Muroran 050-8585, Japan)

  • Haiou Yu

    (School of Applied Mathematics, Jilin University of Finance and Economic, Changchun 130117, China)

Abstract

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.

Suggested Citation

  • Masatomo Takahashi & Haiou Yu, 2022. "Bertrand and Mannheim Curves of Spherical Framed Curves in a Three-Dimensional Sphere," Mathematics, MDPI, vol. 10(8), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1292-:d:792936
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