On the marginally trapped surfaces in Minkowski space-time with finite type Gauss map
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 $\mathbb S^4_1(1)$ or anti-de Sitter space-time $\mathbb H^4_1(-1)$ 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 $\mathbb S^4_1(1)$ or $\mathbb H^4_1(-1)$ with harmonic Gauss map.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2013
- DOI:
- 10.48550/arXiv.1304.5832
- arXiv:
- arXiv:1304.5832
- Bibcode:
- 2013arXiv1304.5832C
- Keywords:
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- Mathematical Physics;
- 53B25;
- 53C40