Spacelike Bertrand curves in Minkowski 3-space revisited

Abstract

In the geometry of curves in 𝔼3, if the principal normal vector field of a given space curve ϕ with non-zero curvatures is the principal normal vector field of another space curve ϕ*, then the curve ϕ is called a Bertrand curve and ϕ* is called Bertrand partner of ϕ. These curves have been studied in di erent space over a long period of time and found wide application in di erent areas. Therefore, we have a great knowledge of geometric properties of these curves. In this paper, revested results for spacelike Bertrand curves with non-null normal vectors will be given with the previous studies on Bertrand curves in 𝔼13. Follow this revested results, the Bertrand curve conditions of a spacelike curve are obtained in 𝔼13. In addition, new curve samples that meet the obtained conditions are constructed and the graphs of these curves are given.

Keywords

• minkowski 3-space
• bertrand curves
• non-null curves
• 53c50
• 53c40