On the quasi-minimal surfaces in the 4-dimensional de Sitter space with 1-type Gauss map

Abstract

In this paper, we study the Gauss map of the surfaces in the de Sitter space-time ${\mathbb{S}}_1^4(1)$. 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.

arXiv commentThis work has been presented in 2nd International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2013)