Journal of the
Korean Mathematical Society JKMS

In this paper, we study surfaces in {3-dimensional} Minkowski space in terms of {certain} {type of} their Gauss map. We give several results on these surfaces whose Gauss map $G$ satisfies $\square G= f(G+C)$ for a smooth function $f$ and a constant vector $C$, where $\square$ denotes the Cheng-Yau operator. In particular, we obtain classification theorems on the rotational surfaces in $\mathbb E^3_1$ with space-like axis of rotation in terms of type of their Gauss map concerning the Cheng-Yau operator.

Keywords: Gauss map, $\square$-pointwise 1-type, Cheng-Yau operator, Minkowski space

MSC numbers: Primary 53B25; Secondary 53C40