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In this paper, we study the Lorentzian minimal surfaces in the Minkowskispace-time with finite type Gauss map. First, we obtain the classification ofthis type of surfaces with pointwise 1-type Gauss map. Then, we proved thatthere are no Lorentzian minimal surface in the Minkowski space-time with null2-type Gauss map.

On the Lorentzian minimal surfaces in $\mathbb E^4_1$ with finite type Gauss map