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Topics on geometry of homogeneous spaces


The proposed project consists of applying Lie theory, in particular semissimple Lie theory, to the study of symplectic and Hermitian geometry of homogeneous spaces.One of the proposed problems is construct examples of mirror manifolds of nilmanifolds, using generalized complex geometry and T-duality (in the sense of Bouwknegt-Hannabuss-Mathai). Other proposed problems are: classification of the invariant generalized complex structures on flag manifolds; the study of the geometry of the moduli space of $J$-holomorphic curves on homogeneous space; and the study of geometric formality on homogeneous space. (AU)

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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)
BALLICO, E.; BARMEIER, S.; GASPARIM, E.; GRAMA, L.; SAN MARTIN, L. A. B.. A Lie theoretical construction of a Landau-Ginzburg model without projective mirrors. MANUSCRIPTA MATHEMATICA, v. 158, n. 1-2, p. 85-101, . (16/22755-1)
DO PRADO, RAFAELA F.; GRAMA, LINO. On the stability of harmonic maps under the homogeneous Ricci flow. COMPLEX MANIFOLDS, v. 5, n. 1, p. 122-132, . (16/22755-1, 12/18780-0)
DEL BARCO, VIVIANA; GRAMA, LINO; SORIANI, LEONARDO. T-duality on nilmanifolds. Journal of High Energy Physics, n. 5, . (15/10937-5, 12/18780-0, 16/22755-1, 15/23896-5, 17/13725-4)
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)
CORREA, EDER M.; GRAMA, LINO. Calabi-Yau metrics on canonical bundles of complex flag manifolds. Journal of Algebra, v. 527, p. 109-135, . (16/22755-1)
DO PRADO, RAFAELA F.; GRAMA, LINO. Variational aspects of homogeneous geodesics on generalized flag manifolds and applications. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, v. 55, n. 3, p. 451-477, . (16/22755-1)

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