Marginally trapped meridian surfaces of parabolic type 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 introduce meridian surfaces of parabolic type as one-parameter systems of meridians of a rotational hypersurface with lightlike axis in Minkowski 4-space and find their basic invariants. We find all marginally trapped meridian surfaces of parabolic type and give a geometric construction of these surfaces.

14 pages. arXiv admin note: substantial text overlap with arXiv:1105.3370

References in corpus (4)

• Invariants and bonnet-type theorem for surfaces in $\r^4$
• Boost invariant marginally trapped surfaces in Minkowski 4-space
• Marginally trapped surfaces in Minkowski 4-space invariant under a rotation subgroup of the Lorentz group
• Chen Rotational Surfaces of Hyperbolic or Elliptic Type in the Four-dimensional Minkowski Space

Cited by in corpus (2)

• Meridian Surfaces of Elliptic or Hyperbolic Type in the Four-dimensional Minkowski Space
• Meridian Surfaces on Rotational Hypersurfaces with Lightlike Axis in ${\mathbb{E}}_2^4$