Spherical curves and Bertrand curves

In this thesis, it is firstly shown that it can be constructed cylindrical helices from the planar curves and Bertrand curves from the spherical curves in 3 dimensional Euclidean space. By using this method, the Bertrand curves corresponding to the spherical indicatrices of a space curve, are investigated. Also, the planar evolute of a cylindrical helice and the spherical evolute of a spherical curve, are studied. The method in Euclidean space is been carried to the Minkowski space and it?s shown that it can be constructed Bertrand curves from the spherical curves in 3 dimensional Minkowski space, too. Also, the hyperbolic evolute of a spherical curve in E is studied. Finally, the Bertrand curves corresponding to the spherical indicatrices of spacelike and timelike curves, are investigated.