Complex curves in R4

In this study, the concepts complex elements and complex curves are extended to the real space R4 which are defined for the real space /?3. In the introduction it is summarized necessary knowledge about the concepts complex elements and complex curves in i?3 and this study is based on these concepts. In the chapter two complex elements and complex curves are defined in the real space R4 and cyclic four-faced is established. In the chapter three minimal elements and minimal curves are defined. Necessary and sufficient conditions are presented for a complex flat to be a minimal flat. Frenet frame is established for a minimal curve in the real space R4, and also it is shown that the tangent vectors and the binormal vectors of the curve are minimal vectors. Also, the cyclic four-faced which is found in the chapter two is expressed with the position vectors of the minimal curves.