Invariant almost Hermitian structures on flag manifolds |
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Authors: | Luiz A.B. San Martin Caio J.C. Negreiros |
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Affiliation: | Instituto de Matemática, Universidade Estadual de Campinas, Cx. Postal 6065, 13.083-970, Campinas - SP, Brazil |
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Abstract: | Let G be a complex semi-simple Lie group and form its maximal flag manifold where P is a minimal parabolic (Borel) subgroup, U a compact real form and T=U∩P a maximal torus of U. We study U-invariant almost Hermitian structures on . The (1,2)-symplectic (or quasi-Kähler) structures are naturally related to the affine Weyl groups. A special form for them, involving abelian ideals of a Borel subalgebra, is derived. From the (1,2)-symplectic structures a classification of the whole set of invariant structures is provided showing, in particular, that nearly Kähler invariant structures are Kähler, except in the A2 case. |
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Keywords: | 53C55 22F30 58E20 |
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