Space-like surfaces on 3-dimensional Minkowski space

This thesis consists of two chapters. In the first chapter some fundamental definitions and theorems are given which will be used in the later chapter. In the two chapter, Construction of a family of space-like surfaces with k1k2 ? m(k1 + k2) = 1. Later, Bäcklund transformation between space-like surfaces with (k1 ? m)(k2 ? m) = l2 and space-like surfaces with (k1 ? m)(k2 ? m) = ?l2 are given. Furthermore, Bäcklund transformation on space-like surfaces with (k1 ?m)(k2 ?m) = ?l2 is given. Key Words: Minkowski 3-Space, Space-like Surfaces, Lax Pair, Sh?Laplace Equation, Bäcklund Transformation