ON THE GAUSS MAP OF TRANSLATION SURFACES IN MINKOWSKI 3-SPACE

Abstract

In this article, we study translation surfaces in the 3-dimensional Minkowski space whose Gauss map $G$ satisfies the condition $\Delta G=AG,A\in {\rm Mat}(3,\Bbb R)$, where $\Delta$ denotes the Laplacian of the surface with respect to the induced metric and Mat(3, ${\Bbb R}$) the set of $3\times 3$ real matrices, and also obtain the complete classification theorem for those.