Translation Surfaces With Pointwise Gauss Map

With the development of mathematics, the basic theory of mathematics has become more and more deeply and perfectly. At the same time, it has also impelled the huge transform method in mathematical research. As the base of all science, mathematics is breaking the traditional aspects and is seeking all areas in human knowledge. As a science of describing physical astrospace, geometry also better reflects different aspects and areas. Now, we not only study geometry in flat space, but also study it in curved space. At present, the most suitable curved space is manifold. One kind of special manifolds is surface. The notion of finite type submanifolds in Euclidean or pseudo-Euclidean space has become an useful tool for investigating and characterizing many important submanifolds. The notion of finite type was extended to differential maps, in particular, to Gauss map of submanifolds. Then we have the conception of pointwise finite type Gauss map.In this thesis we mainly discuss the problem of translation surfaces with pointwise Gauss map. Especially, we study the translation surfaces with pointwise Gauss map. Furthermore, we obtain the conditions for the translation surfaces with pointwise Gauss map.