Abstract
In this paper, we study the Gauss map of the surfaces in the de Sitter space-time S1(1). First, we prove that a space-like surface lying in the de Sitter space-time has pointwise 1-type Gauss map if and only if it has parallel mean curvature vector. Then, we obtain the complete classification of the quasi-minimal surfaces with 1-type Gauss map.
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