Marginally trapped surfaces in spaces of oriented geodesics

Autor(es)

Georgiou, Nikos ^[1] ; Guilfoyle, Brendan ^[2]

Afiliação do(s) autor(es)

^[1] Dept Matemat, BR-05508090 Sao Paulo - Brazil

^[2] Inst Technol Tralee, Dept Comp & Math, Tralee, County Kerry - Ireland

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF GEOMETRY AND PHYSICS; v. 82, p. 1-12, AUG 2014.
• Citações Web of Science: 1

Resumo

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)

• Processo FAPESP: 10/08669-9 - Congruências normais e subvariedades lagrangeanas nos espaços de geodésicas
• Beneficiário: Nikos Georgiou
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado