Space-like surfaces in Minkowski space $E^4_1$ with pointwise 1-type Gauss map

Abstract

We first classify space-like surfaces in the Minkowski space $E^4_1$, de Sitter space $S^3_1$, and hyperbolic space $H^3$ with harmonic Gauss map. Then we give a characterization and classification of space-like surfaces with pointwise 1-type Gauss map of the first kind. We also present some explicit examples.