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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Marginally trapped surfaces in spaces of oriented geodesics

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Author(s):
Georgiou, Nikos [1] ; Guilfoyle, Brendan [2]
Total Authors: 2
Affiliation:
[1] Dept Matemat, BR-05508090 Sao Paulo - Brazil
[2] Inst Technol Tralee, Dept Comp & Math, Tralee, County Kerry - Ireland
Total Affiliations: 2
Document type: Journal article
Source: JOURNAL OF GEOMETRY AND PHYSICS; v. 82, p. 1-12, AUG 2014.
Web of Science Citations: 1
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. (C) 2014 Elsevier B.V. All rights reserved. (AU)

FAPESP's process: 10/08669-9 - Normal Congruences and Lagrangian submanifolds in spaces of geodesics
Grantee:Nikos Georgiou
Support Opportunities: Scholarships in Brazil - Post-Doctoral