On Space-Like Constant Slope Surfaces And Bertrand Curves In Minkowski 3-Space

Abstract

Abstract In the present paper, we define the notions of Lorentzian Sabban frames and de Sitter evolutes of the unit speed space-like curves on de Sitter 2-space 𝕊21. In addi- tion, we investigate the invariants and geometric properties of these curves. Afterwards, we show that space-like Bertrand curves and time-like Bertrand curves can be constructed from unit speed space-like curves on de Sitter 2-space 𝕊21 and hyperbolic space ℍ2, respec- tively. We obtain the relations between Bertrand curves and helices. Also we show that pseudo-spherical Darboux images of Bertrand curves are equal to pseudo-spherical evo- lutes in Minkowski 3-space ℝ31. Moreover we investigate the relations between Bertrand curves and space-like constant slope surfaces in ℝ31. Finally, we give some examples to illustrate our main results.