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Generalized Bertrand Curves of Non-Light-like Framed Curves in Lorentz–Minkowski 3-Space

Author

Listed:
  • Linlin Wu

    (School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China)

  • Anjie Zhou

    (School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China)

  • Kaixin Yao

    (School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China)

  • Donghe Pei

    (School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China)

Abstract

In this paper, we define the generalized Bertrand curves of non-light-like framed curves in Lorentz–Minkowski 3-space; their study is essential for understanding many classical and modern physics problems. Here, we consider two non-light-like framed curves as generalized Bertrand pairs. Our generalized Bertrand pairs can include Bertrand pairs with either singularities or not, and also include Mannheim pairs with singularities. In addition, we discuss their properties and prove the necessary and sufficient conditions for two non-light-like framed curves to be generalized Bertrand pairs.

Suggested Citation

  • Linlin Wu & Anjie Zhou & Kaixin Yao & Donghe Pei, 2024. "Generalized Bertrand Curves of Non-Light-like Framed Curves in Lorentz–Minkowski 3-Space," Mathematics, MDPI, vol. 12(16), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2593-:d:1461616
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