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An extension of the (1,2)-symplectic property for $f$-structures on flag manifolds
N. Cohena, S. Pinzonb a Instituto de Matematica, Estatistica e Computacao Cientifica
b Universidad Industrial de Santander
Abstract:
The (1,1)-symplectic property for $f$-structures on a complex Riemannian
manifold $M$ is a natural extension of the (1,2)-symplectic property for
almost-complex structures on $M$, and arises in the analysis of complex
harmonic maps with values in $M$. A characterization of this property
in combinatorial terms is known only for almost-complex structures or when
$M$ is the classical flag manifold $\mathbb{F}(n)$. In this paper, we
remove these restrictions by considering an intersection graph defined
in terms of the corresponding root system. We prove that the $f$-structure is
(1,1)-symplectic exactly when the intersection graph is locally
transitive. Our intersection graph construction may be helpful
in characterizing many other Kähler-like properties on complex flag
manifolds.
DOI:
https://doi.org/10.4213/im2605
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English version:
Izvestiya: Mathematics, 2008, 72:3, 479–496
Bibliographic databases:
UDC:
514.763.42
MSC: 53C55, 22F30, 17B45, 05C20 Received: 29.12.2006
Citation:
N. Cohen, S. Pinzon, “An extension of the (1,2)-symplectic property for $f$-structures on flag manifolds”, Izv. RAN. Ser. Mat., 72:3 (2008), 69–88; Izv. Math., 72:3 (2008), 479–496
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/izv2605https://doi.org/10.4213/im2605 http://mi.mathnet.ru/eng/izv/v72/i3/p69
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