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Applications of Lie theory in the symplectic and hermitian geometry of homogeneous spaces

Abstract

The proposed project consists of applying Lie theory, in particular semissimple Lie theory, to the study of symplectic and Hermitian geometry of the homogeneous spaces.One of the proposed problems is the study of Lefschetz fibrations on adjoint orbits of semissimple Lie algebras, in order to describe explicitly certain geometric objects such as vanishing cycles and Lefschetz (Lagrangian) thimbles.Other proposed problems are the study of Hermitian structures on generalized flag manifolds in order to extend the results of San Martin-Negreiros, and the study of variational aspects of certain class of geodesics on flag manifolds. (AU)

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Scientific publications
(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)
GRAMA, LINO; NEGREIROS, CAIO J. C.; SAN MARTIN, LUIZ A. B.. Equi-harmonic maps and Plucker formulae for horizontal-holomorphic curves on flag manifolds. Annali di Matematica Pura ed Applicata, v. 193, n. 4, p. 1089-1102, . (12/07482-8)

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