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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2001.tde-20210729-124041
Document
Author
Full name
Albetã Costa Mafra
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2001
Supervisor
Title in Portuguese
Imersões sub-Riemannianas em formas espaciais complexas
Keywords in Portuguese
Geometria Diferencial
Geometria Sub-Riemanniana
Abstract in Portuguese
O objetivo deste trabalho é estudar teoremas de rigidez para um tipo especial de variedades sub-Riemannianas isometricamente imersas em um espaço de formas complexas. Definimos e estudamos algumas características de um tipo especial de geometria sub-Riemanniana. Provamos a existência e unicidade de uma conexão associada à estrutura sub-Riemanniana e a relacionamos com uma determinada conexão de Levi-Civita. Após uma breve revisão da teoria de uma hipervariedade isometricamente imersa em uma variedade Riemanniana e do estudo de um caso particular de submersão Riemanniana, provamos alguns teoremas de rigidez para uma hipervariedade sub-Riemanniana isometricamente imersa em uma forma espacial complexa. Finalizamos analisando o caso de imersões de variedades sub-Riemannianas homogêneas tridimensionais e fazemos alguns exemplos de imersões isométricas
Title in English
not available
Abstract in English
The purpose of this work is to study rigidity theorems for a special type of sub-Riemannian hypersufaces that are isometricaly immersed in complex space forms. We define and study a special type fo sub-Riemannian manifold. We prove the existence and uniqueness of a connection associated with that sub-Riemannian structure and we also relate it to the Levi-civita connection of a metric which is naturally defined from the sub-Riemannian one. After doing a brief review of the theory of isometric immersions of hypersurfaces in Riemannian manifolds and examining a special type of Riemannian submersion we prove theorems related to the rigidity of isometric immersions of sub-Riemannian hypersufaces in comples space forms. We finish this work studying the tridimensional homogeneous sub-Riemannian case and showing some examples of isometric immersions in complex space forms
 
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MafraAlbetaCosta.pdf (8.75 Mbytes)
Publishing Date
2021-07-29
 
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