Invariant generalized complex structures on flag manifolds

Author(s)

Carlos Augusto Bassani Varea

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2020-03-11

Examining board members

Luiz Antonio Barrera San Martin; Lino Anderson da Silva Grama; Gil Ramos Cavalcanti; Lucas Conque Seco Ferreira; Ivan Struchiner

• Advisor: Luiz Antonio Barrera San Martin

Abstract

Generalized complex geometry is a geometrical structure which contains complex and symplectic geometry as special cases. In this thesis, we explore the invariant generalized complex geometry on flag manifolds of semisimple Lie groups. For maximal flag manifolds we describe all invariant generalized almost complex structures. Then, we present which of these structures are integrable, in both the usual (nontwisted) and twisted cases. Using this classification, we describe the action of the Weyl group and the effect of the action by B-transforms on the space of invariant generalized almost complex structures on a maximal flag manifold. We also present a classification of the invariant generalized (almost) Kähler structures. In the case of partial flag manifolds, we present a description of the invariant generalized almost complex structures. Then, we classify which of these structures are integrable for a flag manifold with at most four isotropy summands (AU)

• FAPESP's process: 16/07029-2 - Invariant generalized complex structures on homogeneous spaces
• Grantee: Carlos Augusto Bassani Varea
• Support Opportunities: Scholarships in Brazil - Doctorate