| Grant number: | 15/23896-5 |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| Start date: | May 01, 2016 |
| End date: | April 30, 2019 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
| Principal Investigator: | Luiz Antonio Barrera San Martin |
| Grantee: | Viviana Jorgelina Del Barco |
| Host Institution: | Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil |
| Associated research grant: | 12/18780-0 - Geometry of control systems, dynamical and stochastics systems, AP.TEM |
| Associated scholarship(s): | 17/13725-4 - Locally conformal geometry on flag manifolds, BE.EP.PD |
Abstract This research project proposes to study geometric structures on real flag manifolds. Flag manifolds are homogeneous manifolds of the form $\F_\Theta=G/P$ where $G$ is a semi-simple Lie group and $P$ is a parabolic subgroup of $G$. In addition they admit a presentation as $\F_\Theta=K/K_\Theta$ where $K$ is a maximal compact subgroup of $G$. It is of our interest to study the existence of symplectic structures and pseudo-Riemannian metrics on $\F_\Theta$ which remain invariant under the action of $K$ and/or $G$.When $G$ is a complex Lie group $\F_\Theta$ is a complex manifold, its structure is well understood and it is well known that its geometry is very rich. Instead we propose to consider real flag manifolds for which many geometrical questions remain open. Particularly we are interested in symplectic flag manifolds.Moreover, through the understanding of the geometry of real flag manifolds, we intend to answer open conjectures in the field of pseudo-Riemannian manifolds whose geodesics are orbits of one parameter subgroups. | |
| News published in Agência FAPESP Newsletter about the scholarship: | |
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