Classification of Translation Surfaces of Type 1 in Semi-Isotropic Space

In this paper, we classify translation surfaces of Type1 in the threedimensional semi- isotropic space {SI}^{3} under the condition Delta ^{J}x_{i}=\lambda _{i}x_{i}, where \Delta ^{J} denotes the Laplacian of the surface with respect to the first, the second and the third fundamental forms. We also give explicit forms of these surfaces.