An invariant theory of marginally trapped surfaces in the four-dimensional Minkowski space

Details An invariant theory of marginally trapped surfaces in the four-dimensional Minkowski space An invariant theory of marginally trapped surfaces in the four-dimensional Minkowski space

2011-05-17

arxiv.org/abs/1105.3370v1

Mathematics

Differential Geometry

16 pages

Scientific paper

A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. We associate a geometrically determined moving frame field to such a surface and using the derivative formulas for this frame field we obtain seven invariant functions. Our main theorem states that these seven invariants determine the surface up to a motion in Minkowski space. We introduce meridian surfaces as one-parameter systems of meridians of a rotational hypersurface in the four-dimensional Minkowski space. We find all marginally trapped meridian surfaces.

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