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

2013/11/07 by Turgay, Nurettin Cenk
#53B25 #53C50 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1311.1962

Abstract

In this paper, we study the Gauss map of the surfaces in the de Sitter space-time \mathbb S⁴₁(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.

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