A characterization of some surfaces given with the monge patch

In this thesis, the surfaces given with the Monge patch are considered. Conclusions about translation are mentioned and the original results are obtained for the translation-factorable surfaces which are considering by both of the translation and factorable surfaces. This thesis consists of five chapters. The first section is the introduction. In the second section, general information about the differential geometry of surfaces in Euclidean space is given. Further some basic definitions and concepts are concerned about surfaces having finite type coordinates. In the third section, surfaces in 3 and 4 dimensional Euclidean space given with the Monge patch, translation surfaces and factorable surfaces are introduced. The curvatures of these surfaces are obtained. Furthermore the classification theorems on the conditions of being flat and minimal are given. In the fourth section, TF (translation-factorable) surfaces, in 3 and 4 dimensional Euclidean space which are obtained with the help of translation and factorable surfaces, are introduced. The Gaussian and mean curvature of these surfaces is calculated. Also a classification theorems for become flat and minimal of these TF type surfaces are given. However, the Laplacian of the surfaces given with the Monge patch and TF type surfaces are calculated and the conditions of finite type coordinates are obtained in . The fifth section is the conclusion of the thesis.