Classification of marginally trapped Lorentzian flat surfaces in E42 and its application to biharmonic surfaces

A surface in a semi-Riemannian manifold is called marginally trapped if its mean curvature vector field is light-like at each point. In this article, we classify marginally trapped Lorentzian flat surfaces in the pseudo-Euclidean space E42 . As an application, we obtain the complete classification of biharmonic Lorentzian surfaces in E42 with light-like mean curvature vector. © 2007 Elsevier Inc. All rights reserved.