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

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