Ulisse Dini type helicoidal hypersurface in Euclidean four space

This master thesis consists of six chapters. In the first chapter, the historical process of the studies and developments in the theory of minimal surfaces are mentioned. In the second chapter, some basic definitions and concepts are given. In the third chapter, Dini helicoidal surface in 3-dimensional Euclidean space is given. The mean and the Gaussian curvatures of Dini helicoidal surface are calculated. In the fourth chapter, a minimal helicoidal surface of Dini type is given. In this section, minimality condition of the Dini type helicoidal surface are shown in a theorem. In the fifth chapter, the helicoidal hypersurface of Dini type in the four dimensional Euclidean space is given. The Gaussian curvature and the mean curvature of the hypersurface are calculated, and special relations and symmetries of curvatures are obtained. In the sixth and last section, there are results and suggestions.