On the Quasi-Minimal Surfaces in the 4-Dimensional de Sitter Space With 1-Type Gauss Map - Turgay, Nurettin Cenk (Sarajevo Journal of Mathematics, 2015)
In this paper, we study the Gauss map of the surfaces in the de Sitter space-time $\mathbb S^4_1(1)$. First, we prove that a space-like surface lying in the de Sitter space-time has pointwise 1-type Gauss map if and only if it has parallel mean curvature vector. Then, we obtain the complete classification of the quasi-minimal surfaces with 1-type Gauss map. 2010 Mathematics Subject Classification. 53B25, 53C50.