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arXiv · 1311.1962

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

Nurettin Cenk Turgay
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Abstract

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.

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Nurettin Cenk Turgay. 2013-11-07. On the quasi-minimal surfaces in the 4-dimensional de Sitter space with 1-type Gauss map. https://arxiv.org/abs/1311.1962

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