Curvatures and some characterizations of translation surfaces

This thesis consists of six chapters. The first chapter is devoted to the introduction. The second chapter, concepts and definitions which are needed in the further chapters are given. The third chapter, some calculations about the coefficients of the first and second fundamental forms, the shape operator matrix, the mean curvature, the Gaussian curvature, the principal curvatures of the translation surface have been made. The fourth chapter, a classification of some special points of the translation surface is given. The fifth chapter, the translation surfaces generated by the spherical indicatrix curves are defined. Some characterizations about the translation surfaces generated by the tangents, principal normals and binormals indicatrices curves have been obtained, respectively. In the last chapter, the results obtained from the thesis are given.