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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2008.tde-01072008-163534
Document
Author
Full name
Fernando Manfio
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2008
Supervisor
Committee
Piccione, Paolo (President)
Lima, Levi Lopes de
Mercuri, Francesco
Tausk, Daniel Victor
Veloso, Jose Miguel Martins
 
Title in Portuguese
Imersões isométricas em 3-variedades Lorentzianas homogêneas
Keywords in Portuguese
G-estruturas
Imersões isométricas
Rigidez isométrica.
Abstract in Portuguese
Neste trabalho, provamos um teorema de imersões isométricas em variedades Lorentzianas homogêneas tridimensionais, usando a teoria de G- estruturas. Tais variedades são aquelas consideradas na classificação das 3- variedades Lorentzianas homogêneas de Dumitrescu e Zeghib. Provamos também um teorema de rigidez isométrica para hipersuperfícies em variedades semi-Riemannianas com G-estrutura infinitesimalmente homogêneas. No caso particular em que o ambiente são variedades semi-Riemannianas dadas por produto de uma forma espacial por R ou variedades Riemannianas homogêneas tridimensionais, provamos o mesmo teorema de rigidez isométrica, porém com hipóteses mais fracas.
 
Title in English
Isometric immersions into 3-dimensional Lorentzians homogeneous manifolds
Keywords in English
G-structures
Isometric embeddings
isometric rigidity.
Abstract in English
In this work we prove an isometric embedding theorem in homogeneous Lorentzian manifolds of dimension 3, that were recently classified by Dumitrescu and Zeghib in [11]. We also prove a rigidity result of isometric embeddings of hypersurfaces in semi-Riemannian manifolds endowed with an infinitesimally homogeneous G-structure. In the special case that the semi-Riemannian manifolds are produtcs of the type Q^n_cxR, or Riemannian homogeneous 3-manifolds, the result is proven under wear assumptions.
 
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Publishing Date
2012-05-29
 
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