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Title: Classification of marginally trapped surfaces with parallel mean curvature vector in Lorentzian space forms
Authors: Chen, Bang-Yen ×
Van der Veken, Joeri #
Issue Date: 2010
Publisher: Univ houston
Series Title: Houston journal of mathematics vol:36 issue:2 pages:421-449
Abstract: A space-like surface in a 4D Lorentzian manifold is called marginally trapped if its mean curvature vector is light-like at each point. In this article, we completely classify marginally trapped surfaces with parallel mean curvature vector in 4D Lorentzian space forms. Our main results state that there are six families of such surfaces in the Minkowski space-time, eight families in the anti-de Sitter space-time. Conversely, marginally trapped surfaces with parallel mean curvature vector in 4D Lorentzian space forms are obtained from these families. Explicit examples of such surfaces are presented. In addition we give a simple relation between marginally trapped surfaces with parallel mean curvature vector and biharmonic surfaces in 4D Minkowski space-time E^4_1.
ISSN: 0362-1588
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Geometry Section
× corresponding author
# (joint) last author

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