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| Author(s): |
Leonardo Soriani Alves
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2015-03-27 |
| Examining board members: |
Luiz Antonio Barrera San Martin;
Diego Sebastian Ledesma;
Henrique Bursztyn
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| Advisor: | Luiz Antonio Barrera San Martin; Lino Anderson da Silva Grama |
| Abstract | |
We study generalized complex geometry, which encompasses complex and symplectic geometry as particular cases. We begin with the algebraic basics on a vector space and then we transport these concepts to manifolds. We study the Courant bracket on the direct sum of tangent and cotangent bundles of a manifold, which is essential to define the integrability of the generalized complex structures. We check that on every $6$ dimensional nilmanifolds there is a left invariant generalized complex structure, even though some of them do not admit complex or symplectic structure. We study two notions of T-dualidade and its relations to generalized complex geometry. We recall mirror symmetry for elliptic curves and derive a manifestation of mirror symmetry from generalized complex geometry (AU) | |
| FAPESP's process: | 13/04034-7 - Hermitian structures and generalized complex geometry on homogeneous space. |
| Grantee: | Leonardo Soriani Alves |
| Support Opportunities: | Scholarships in Brazil - Master |