Time-like constant slope surfaces and space-like Bertrand curves in Minkowski 3-space

摘要

Defining Lorentzian Sabban frame of the unit speed time-like curves on deSitter 2-space $\mathbb{S}^{2}_{1}$ and introducing space-like height functionon the unit speed time-like curves on $\mathbb{S}^{2}_{1}$, the invariants ofthe unit speed time-like curves on $\mathbb{S}^{2}_{1}$ and geometricproperties of de Sitter evolutes of the unit speed time-like curves on$\mathbb{S}^{2}_{1}$ are studied. A relation between space-like Bertrand curvesand helices is obtained. De Sitter Darboux images of space-like Bertrand curvesare equal to de Sitter evolutes. The relations between time-like constant slopesurfaces lying in the space-like cone and space-like Bertrand curves inMinkowski 3-space $\mathbb{R}^{3}_{1}$ are obtained.