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

Abstract

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.

16 pages

References in corpus (6)

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Cited by in corpus (7)

• Marginally trapped meridian surfaces of parabolic type in the four-dimensional Minkowski space
• Marginally trapped surfaces with pointwise 1-type Gauss map in Minkowski 4-space
• Meridian Surfaces of Elliptic or Hyperbolic Type in the Four-dimensional Minkowski Space
• Meridian Surfaces with Constant Mean Curvature in Pseudo-Euclidean 4-space with Neutral Metric
• Fundamental Theorems for Timelike Surfaces in the Minkowski 4-Space
• Quasi-minimal Rotational Surfaces in Pseudo-Euclidean Four-dimensional Space
• Meridian Surfaces on Rotational Hypersurfaces with Lightlike Axis in ${\mathbb{E}}_2^4$