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Master's Dissertation
DOI
10.11606/D.45.2018.tde-04042018-132823
Document
Author
Full name
Ivo Terek Couto
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2018
Supervisor
Committee
Lymberopoulos, Alexandre (President)
Manfio, Fernando
Ribeiro, Pedro Lauridsen
Title in Portuguese
Caracterizações de subvariedades marginalmente aprisionadas em formas espaciais
Keywords in Portuguese
Geometria Lorentziana
Relatividade geral
Superfícies marginalmente aprisionadas
Abstract in Portuguese
Neste trabalho, estudamos as subvariedades das formas espaciais pseudo-Riemannianas M^n_v(c) com vetor curvatura média de tipo luz, chamadas marginalmente aprisionadas, explorando as relações desta condição (motivada pela Física) com várias outras hipóteses de caráter geométrico, como lambda-isotropia, presença de nulidade relativa e invariância por um certo grupo de transformações de Lorentz. Em particular, apresentamos vários resultados de classificação e rigidez de superfícies marginalmente aprisionadas nos espaços de Lorentz-Minkowski L^4, de Sitter S^4_1 e anti-de Sitter H^4_1 nestes contextos, adaptando e generalizando resultados de alguns artigos.
Title in English
Characterizations of marginally trapped submanifolds in space-forms
Keywords in English
General relativity
Lorentz geometry
Marginally trapped surfaces
Abstract in English
In this work, we study the submanifolds of pseudo-Riemannian space forms M^n_v(c) with lightlike mean curvature vector, called marginally trapped, exploring the relations of this condition (motivated by Physics) with several other assumptions of geometric character, such as \lambda-isotropy, presence of relative nullity and invariance by a certain group of Lorentz transformations. In particular, we prove several ridigity and classification results for marginally trapped surfaces in Lorentz-Minkowski space L^4, de Sitter space S^4_1 and anti-de Sitter space H^4_1 in these settings, adapting and generalizing results from several papers.
 
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diss.pdf (1.10 Mbytes)
Publishing Date
2018-04-16
 
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