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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2016.tde-05102015-104320
Document
Author
Full name
Maikel Antonio Samuays
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2015
Supervisor
Committee
Chaves, Rosa Maria dos Santos Barreiro (President)
Anciaux, Henri Nicolas Guillaume
Brito, Fabiano Gustavo Braga
Camargo, Fernanda Ester Camillo
Sousa Junior, Luiz Amancio Machado de
Title in Portuguese
Subvariedades lagrangeanas mínimas e autossimilares no espaço paracomplexo
Keywords in Portuguese
Espaço paracomplexo
Subvariedades autossimilares
Subvariedades lagrangeanas
Abstract in Portuguese
Neste trabalho estudamos as subvariedades lagrangeanas mínimas e autossimilares do espaço paracomplexo Dn. Começamos definindo o conceito de variedade para-Kähler e, como exemplo, descrevemos o espaço projetivo paracomplexo. Em seguida, estudamos as subvariedades paracomplexas e lagrangeanas. Após mostrarmos que toda subvariedade paracomplexa não-degenerada é mínima, dedicamos a atenção ao estudo das subvariedades lagrangeanas, restringindo-nos ao ambiente Dn. Em particular, estudamos as lagrangeanas que são invariantes sob a ação canônica do grupo SO(n), e as superfícies de Castro-Chen. Em ambos os casos, analisamos a minimalidade e a autossimilaridade das mesmas.
Title in English
Minimal and self-similar Lagrangian submanifolds in the para-complex space
Keywords in English
Lagrangian submanifolds
Para-complex space
Self-similar submanifolds.
Abstract in English
In this work, we study minimal and self-similar Lagrangian submanifolds in the para-complex space Dn. Firstly, we define the concept of para-Kähler manifold and, to exemplify, we describe the para-complex projective space.Then, we study para-complex submanifolds and Lagrangian submanifolds. After proving that every non-degenerate para-complex submanifold is minimal, we pay attention to Lagrangian submanifolds, restricting us to the case of Dn. In particular, we study Lagrangian submanifolds which are invariant by the canonical SO(n)-action of Dn, and Castro-Chen's surfaces. In both cases, we analyse the minimality and self-similarity.
 
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Principal.pdf (1.19 Mbytes)
Publishing Date
2016-03-10
 
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