Marginally trapped surfaces in spaces of oriented geodesics |
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Institution: | 1. Departamento de Matematica, Rua do Matão, 1010 Cidade Universitaria - São Paulo, SP - CEP 05508-090, Brazil;2. Institute of Technology Tralee, Department of Computing and Mathematics, Clash, Tralee, County Kerry, Ireland |
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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. |
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Keywords: | Marginally trapped surface Mean curvature Neutral Kähler structure Spaces of geodesics |
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