On the marginally trapped surfaces in Minkowski space-time with finite type Gauss map

2013/04/22 by Turgay, Nurettin Cenk
#53B25 #53C40 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1304.5832

Abstract

In this paper, we work on the marginally trapped surfaces in the 4-dimensional Minkowski, de Sitter and anti-de Sitter space-times. We obtain the complete classification of the marginally trapped surfaces in the Minkowski space-time with pointwise 1-type Gauss map. Further, we give construction of marginally trapped surfaces with 1-type Gauss map and a given boundary curve. We also state some explicit examples. We also prove that a marginally trapped surface in the de Sitter space-time \mathbb S⁴₁(1) or anti-de Sitter space-time \mathbb H⁴₁(-1) has pointwise 1-type Gauss map if and only if its mean curvature vector is parallel. Moreover, we obtain that there exists no marginally trapped surface in \mathbb S⁴₁(1) or \mathbb H⁴₁(-1) with harmonic Gauss map.

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