Imaginary curves

This master thesis consists of four main parts. The first part consists of the introduction. In the introduction, the history of curves and virtual curves is mentioned. For a better understanding of the subject, it is mentioned that minimal surfaces belong to complex curves and that they are isotropic. The second part is reserved for the history of the literature and in this part, the basic concepts are explained. In the third chapter, definitions and theorems about imaginary elements are given. In the third chapter, the imaginary point, the imaginary point at infinity, the imaginary plane in real space, the single line passing through the imaginary point, the conjugate real line connecting two lines, the conjugate imaginary lines, and the imaginary plane in real space are explained. In addition, E. Cartan cyclic trihedron was examined. In the fourth chapter, the virtual curve is first defined and it is shown that this curve can be an isotropic curve.