Marginally trapped surfaces in Minkowski 4-space invariant under a rotation subgroup of the Lorentz group

摘要

A local classification of spacelike surfaces in Minkowski 4-space, which are invariant under spacelike rotations, and with mean curvature vector either vanishing or lightlike, is obtained. Furthermore, the existence of such surfaces with prescribed Gaussian curvature is shown. A procedure is presented to glue several of these surfaces with intermediate parts where the mean curvature vector field vanishes. In particular, a local description of marginally trapped surfaces invariant under spacelike rotations is exhibited. Keywords Lightlike mean curvature vector - Marginally trapped surfaces - Lorentz group S. Haesen was partially supported by the Research Foundation—Flanders project G.0432.07. S. Haesen and M. Ortega were partially supported by the Spanish MEC Grant MTM2007-60731 with FEDER funds and the Junta de Andalucía Regional Grant P06-FQM-01951. This work was started when S. Haesen was a postdoctoral researcher at the Section of Geometry of the Katholieke Universiteit Leuven.