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Invariant structures on real flag manifolds

Grant number: 15/23896-5
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): May 01, 2016
Effective date (End): 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


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.

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Scientific publications (6)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
DEL BARCO, VIVIANA; BARRERA SAN MARTIN, LUIZ ANTONIO. De Rham 2-Cohomology of Real Flag Manifolds. Symmetry Integrability and Geometry-Methods and Applications, v. 15, . (17/13725-4, 12/18780-0, 15/23896-5)
FREITAS, ANA P. C.; DEL BARCO, VIVIANA; SAN MARTIN, LUIZ A. B.. Invariant almost complex structures on real flag manifolds. Annali di Matematica Pura ed Applicata, v. 197, n. 6, p. 1821-1844, . (17/13725-4, 12/18780-0, 15/23896-5)
DEL BARCO, VIVIANA; GRAMA, LINO; SORIANI, LEONARDO. T-duality on nilmanifolds. Journal of High Energy Physics, n. 5, . (15/10937-5, 15/23896-5, 17/13725-4, 12/18780-0, 16/22755-1)
DEL BARCO, VIVIANA; GRAMA, LINO. On generalized G(2)-structures and T-duality. JOURNAL OF GEOMETRY AND PHYSICS, v. 132, p. 109-113, . (17/13725-4, 16/22755-1, 12/18780-0, 15/23896-5)
DEL BARCO, VIVIANA; GRAMA, LINO; SORIANI, LEONARDO. T-duality on nilmanifolds. Journal of High Energy Physics, v. N/A, n. 5, p. 25-pg., . (15/23896-5, 12/18780-0, 17/13725-4, 16/22755-1, 15/10937-5)
DEL BARCO, VIVIANA; MOROIANU, ANDREI. Killing Forms on 2-Step Nilmanifolds. JOURNAL OF GEOMETRIC ANALYSIS, v. 31, n. 1, . (15/23896-5)

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