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

Linlin Wu, Anjie Zhou, Kaixin Yao and Donghe Pei ()
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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

Mathematics, 2024, vol. 12, issue 16, 1-12

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.

Keywords: Lorentz–Minkowski space; generalized Bertrand curve; framed curve; singularity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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