• Journal of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.381-397
• /
• 2017

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 ChengYau 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.