Minimal and self-similar Lagrangian submanifolds in the para-complex space

Author(s)

Maikel Antonio Samuays

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2015-07-23

Examining board members

Rosa Maria dos Santos Barreiro Chaves; Henri Nicolas Guillaume Anciaux; Fabiano Gustavo Braga Brito; Fernanda Ester Camillo Camargo; Luiz Amancio Machado de Sousa Junior

• Advisor: Rosa Maria dos Santos Barreiro Chaves

Abstract

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. (AU)

• FAPESP's process: 12/02724-3 - Minimal and self-similar Lagrangian submanifolds in complex and para-complex pseudo-Euclidean spaces
• Grantee: Maikel Antonio Samuays
• Support Opportunities: Scholarships in Brazil - Doctorate