Marginally trapped surfaces in spaces of oriented geodesics
arXiv:1305.6600 · doi:10.1016/j.geomphys.2014.03.012
Abstract
We investigate the geometric properties of marginally trapped surfaces (surfaces which have null mean curvature vector) in the spaces of oriented geodesics of Euclidean 3-space and hyperbolic 3-space, endowed with their canonical neutral Kaehler structures. We prove that every rank one surface in these four manifolds is marginally trapped. In the Euclidean case we show that Lagrangian rotationally symmetric sections are marginally trapped and construct an explicit family of marginally trapped Lagrangian tori. In the hyperbolic case we explore the relationship between marginally trapped and Weingarten surfaces, and construct examples of marginally trapped surfaces with various properties.
15 pages, 1 figure
References in corpus (4)
- On the Geometry of Spaces of Oriented Geodesics
- A characterization of Weingarten surfaces in hyperbolic 3-space
- Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface
- Marginally trapped submanifolds in Lorentzian space forms and in the Lorentzian product of a space form by the real line