Abstract
By using moving frames and directred digraphs, we study invariant (1,2)-symplectic structures on complex flag manifolds. Let $F$ be a flag manifold with height $k-1$. We show that there is a $k$-dimensional family of invariant (1,2)-symplectic metrics of any parabolic structure on $F$. We also prove any invariant almost complex structure $J$ on $F$ with height 4 admits an invariant (1,2)-symplectic metric if and only if $J$ is parabolic or integrable.
Citation
Xiaohuan Mo. Caio J. C. Negreiros. "$(1,2)$-symplectic structures on flag manifolds." Tohoku Math. J. (2) 52 (2) 271 - 282, 2000. https://doi.org/10.2748/tmj/1178224611
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