On space-like surfaces in Minkowski 4-space with pointwise 1-type Gauss map of the second kind

In this work, we study space-like surfaces in the Minkowski space E{double-struck} ⁴ ₁ with pointwise 1-type Gauss map. We prove that a maximal surface in E{double-struck} ⁴ ₁ has pointwise 1-type Gauss map of the second kind if and only if it is an open part of a space-like plane. We also give a classification of surfaces in E{double-struck} ⁴ ₁ with flat normal bundle, non-zero constant curvature and pointwise 1-type Gauss map of the second kind.