The original part of this thesis is the study of Gauss map on a new type of tubular surface based on [22, 28]. The concept of finite type immersions was interoduced by Chen in 1981 ([15]). Then he writes some papers related to this topic. An isometric immersion x : M ? E^m for a submanifold M of an Euclidean space E^m that also known as the position vector field of M, is called as a finite type, if it is written as a finite sum of eigenvectors of the Laplacian ? of M for a constant map x0, and non-constant maps x1,x2,...,xk,i.e.,x = x0 #43;?k i=1 xi. If the eigenvectors of the Laplacian are different numbers, then the submanifold is called as k-type. This term is extended to the Laplacian of Gauss map of M as ?G = a(G #43; C) for a real number a and a constant vector C by Chen and Piccinni in [19]. The Gauss map G of a submanifold that satisfies in above relation is called of 1?type Gauss map.
