Complete Space-like λ-surfaces in the Minkowski Space R_1~3 with the Second Fundamental Form of Constant Length

In this paper we study the complete space-like λ-surfaces in the three dimensional Minkowski space R_1~3. As the result, we obtain a complete classification theorem for all the complete space-like λ-surfaces x : M~2→ R_1~3 with the second fundamental form of constant length. This is a natural extension to the λ-surfaces in R_1~3 of a recent interesting classification theorem by Cheng and Wei for λ-surfaces in the Euclidean space R~3.