Author(s): Santos, Jo??o Batista Marques dos
Date: 2018
Origin: Oasisbr
Subject(s): Variedades Homog??neas Tridimensionais; Superf??cies totalmente umb??licas; Grupos de Lie unimodulares; Grupos de Lie n??o-unimodulares; Homogeneous 3-manifolds; Totally umbilical surfaces; Unimodular Lie groups; Non-unimodular Lie groups; CI??NCIAS EXATAS E DA TERRA: MATEM??TICA: GEOMETRIA E TOPOLOGIA: GEOMETRIA DIFERENCIAL
Submitted by Jo??o Santos (joaobatistauea2012@gmail.com) on 2018-11-30T21:01:29Z No. of bitstreams: 4 Disserta????o Jo??o Marques Batista dos Santos.pdf: 543401 bytes, checksum: 4541b8b09d0d4039139f35aa8985aadb (MD5) Ata de Defesa - Jo??o Batista (1).pdf: 866752 bytes, checksum: 321c54d256c356c0d52095cf06dcbe2c (MD5) Folha de Aprova????o - Jo??o Batista.pdf: 446744 bytes, checksum: f0cfa5935e042cea772148a21b280c58 (MD5) Carta de encaminhamento - Jo??o Batista.pdf: 318150 bytes, checksum: a3df23929f8484ee602220dfef1e9d90 (MD5)
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Rejected by Divis??o de Documenta????o/BC Biblioteca Central (ddbc@ufam.edu.br), reason: A Disserta????o depositada est?? sem a Ficha Catalogr??fica. Um novo documento deve ser depositado com Ficha Catalogr??fica. Segue link... http://biblioteca.ufam.edu.br/servicos/elaboracao-de-ficha-catalografica D??vidas? ddbc@ufam.edu.br on 2018-12-03T17:34:38Z (GMT)
Rejected by Divis??o de Documenta????o/BC Biblioteca Central (ddbc@ufam.edu.br), reason: A Disserta????o depositada est?? sem a Ficha Catalogr??fica. Um novo documento deve ser depositado com Ficha Catalogr??fica. Segue link... http://biblioteca.ufam.edu.br/servicos/elaboracao-de-ficha-catalografica D??vidas? ddbc@ufam.edu.br on 2018-12-03T17:35:26Z (GMT)
Rejected by Divis??o de Documenta????o/BC Biblioteca Central (ddbc@ufam.edu.br), reason: A Disserta????o depositada est?? sem a Ficha Catalogr??fica. Um novo documento deve ser depositado com Ficha Catalogr??fica. Segue link... http://biblioteca.ufam.edu.br/servicos/elaboracao-de-ficha-catalografica D??vidas? ddbc@ufam.edu.br on 2018-12-03T17:33:31Z (GMT)
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Rejected by Divis??o de Documenta????o/BC Biblioteca Central (ddbc@ufam.edu.br), reason: A disserta????o depositada est?? sem a Ficha Catalogr??fica. A ficha pode ser feita em http://biblioteca.ufam.edu.br/servicos/elaboracao-de-ficha-catalografica d??vidas? ddbc@ufam.edu.br on 2018-12-20T17:58:16Z (GMT)
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Made available in DSpace on 2018-12-20T19:05:09Z (GMT). No. of bitstreams: 4 Ata de Defesa - Jo??o Batista (1).pdf: 866752 bytes, checksum: 321c54d256c356c0d52095cf06dcbe2c (MD5) Folha de Aprova????o - Jo??o Batista.pdf: 446744 bytes, checksum: f0cfa5935e042cea772148a21b280c58 (MD5) Carta de encaminhamento - Jo??o Batista.pdf: 318150 bytes, checksum: a3df23929f8484ee602220dfef1e9d90 (MD5) Disserta????o Jo??o Marques Batista dos Santos.pdf: 992792 bytes, checksum: 964ec1d5465551c0aa8e0ca6f0995ec4 (MD5) Previous issue date: 2018-08-17
CAPES - Coordena????o de Aperfei??oamento de Pessoal de N??vel Superior
92994746870
In this dissertation, we studied the complete classification of totally umbilical surfaces immersed in homogeneous 3-manifolds, as obtained in the article entitled "The classification of totally umbilical surfaces in homogeneous 3-manifolds" by Manzano and Soaum [Math. Z. 279 (2015) 557-576]. In the case of unimodular Lie groups it was shown that, except for the Euclidean space R3, unit sphere S3, soluble group Sol3 and the totally geodesics examples that appear in some special cases given by Tsukada [Kodai Math. J. 19 (3) (1996) 395-437], there are no fully umbilical surfaces. Moreover, there were obtained herein extensions of some results of Inoguchi and Van der Veken [Geom. Dedicata. 131 (2008) 159-172], Souam and Toubiana [Math. Helv. 84 (3) (2009) 673-704] and Tsukada [Kodai Math. J. 19 (3) (1996) 395-437], giving alternative proves for each case. In the case of non-unimodular Lie groups, the totally umbilical surfaces exist when the Lie group is isometric to the hyperbolic space H3 and to the product space H2 x R. Futhermore, in some special cases of non-unimodular Lie groups it was shown, up to ambient isometries, the existence of complete totally geodesics surfaces and complete totally umbilical one which are not totally geodesics.
Nesta disserta????o, estudamos a classifica????o completa das superf??cies totalmente umb??licas imersas em variedades homog??neas tridimensionais, obtida no artigo intitulado "The classification of totally umbilical surfaces in homogeneous 3-manifolds" por Manzano e Souam [Math. Z. 279 (2015) 557-576]. Nos grupos de Lie unimodulares foi mostrado que, exceto para o espa??o Euclidiano R3, a esfera unit??ria S3, o grupo sol??vel Sol3 e os exemplos totalmente geod??sicos que aparecem em alguns casos especiais dados por Tsukada [Kodai Math. J. 19 (3) (1996) 395-437], n??o existem superf??cies totalmente umb??licas. Al??m disso, foi obtido extens??es de alguns resultados de Inoguchi e Van der Veken [Geom. Dedicata. 131 (2008) 159-172], Souam e Toubiana [Math. Helv. 84 (3) (2009) 673-704] e Tsukada [Kodai Math. J. 19 (3) (1996) 395-437], dando provas alternativas para cada caso. Nos grupos de Lie n??o-unimodulares, as superf??cies totalmente umb??licas existem nos casos em que o grupo de Lie ?? isom??trico ao espa??o hiperb??lico H3 e ao espa??o produto H2(k)xR. Al??m disso, em alguns casos especiais de grupos de Lie n??o-unimodulares foi mostrado, a menos de uma isometria do espa??o ambiente, a exist??ncia de superf??cies completas totalmente geod??sicas e superf??cies completas totalmente umb??licas que n??o s??o totalmente geod??sicas.
