Marginally Trapped Surfaces in Spaces of Oriented Geodesics

Authors

Nikos Georgiou, Departamento de Matematica, Rua do Matão, 1010 Cidade Universitaria - São Paulo, SP - CEP 05508-090, Brazil.
BRENDAN GUILFOYLE, School of Science, Technology, Engineering and Mathematics, Institute of Technology, Tralee, Clash, Tralee, Co. Kerry, Ireland.Follow

Document Type

Article

Disciplines

Mathematics

Publication Details

Journal of Geometry and Physics

© 2014 Elsevier B.V.

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.

Recommended Citation

Nikos Georgiou, Brendan Guilfoyle, Marginally trapped surfaces in spaces of oriented geodesics, Journal of Geometry and Physics, Volume 82, 2014, Pages 1-12, ISSN 0393-0440, https://doi.org/10.1016/j.geomphys.2014.03.012.