On the marginally trapped surfaces in 4-dimensional space-times with finite type Gauss map


Turgay N. C.

GENERAL RELATIVITY AND GRAVITATION, vol.46, no.1, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 1
  • Publication Date: 2014
  • Doi Number: 10.1007/s10714-013-1621-y
  • Title of Journal : GENERAL RELATIVITY AND GRAVITATION

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 a construction of a marginally trapped surface with 1-type Gauss map with a given boundary curve. We also state some explicit examples. We also prove that a marginally trapped surface in the de Sitter space-time S-1(4) (1) or anti-de Sitter space-time H-1(4) (-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 S-1(4) (1) or H-1(4) (-1) with harmonic Gauss map.