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Doctoral Thesis
DOI
10.11606/T.45.2012.tde-16072012-174434
Document
Author
Full name
Jaime Leonardo Orjuela Chamorro
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2012
Supervisor
Committee
Gorodski, Claudio (President)
Figueiredo Junior, Ruy Tojeiro de
Jardim, Marcos Benevenuto
Mercuri, Francesco
Silva, Marcos Martins Alexandrino da
Title in Portuguese
Hipersuperfícies mínimas e completas de espaços simétricos
Keywords in Portuguese
Ações polares
Espaços simétricos
Geometria diferencial equivariante
Hipersuperfícies mímimas
Abstract in Portuguese
No presente trabalho construímos novos exemplos de hipersuperfícies mínimas, completas e H-equivariantes de espaços simétricos. Para tal, usamos o método da geometria diferencial equivariante (Hsiang-Lawson). Dividimos nosso estudo em duas partes, a saber, espaços simétricos G/K de tipo não compacto e compacto. No primeiro caso são estudadas ações polares de subgrupos H adaptados à decomposição de Iwasawa G=KAN. No segundo caso usamos a classificação (Podesta-Thobergsson) dos subgrupos H de Spin(9) que atuam com cohomogeneidade dois sobre o plano projetivo octoniônico F_4/Spin(9).
Title in English
Complete minimal hipersurfaces in symmetric spaces
Keywords in English
Equivariant differential geometry
Minimal hypersurfaces
Polar actions
Symmetric spaces
Abstract in English
In the present work we construct new examples of complete minimal H-equivariant hypersurfaces of symmetric spaces G/K. For that, we use the equivariant differential geometry method (Hsiang-Lawson). We divide our research in two parts, namely, symmetric spaces of non-compact and compact type. In the first case we study polar actions of subgroups H adapted to the Iwasawa decomposition G=KAN. In the second case we use the classification (Podesta-Thobergsson) of the subgroups H of Spin(9) which act with cohomogeneity two on the octonionc projective plane F_4/Spin(9).
 
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Publishing Date
2012-07-19
 
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