$(1,2)$-symplectic structures on flag manifolds
Mo, Xiaohuan ; Negreiros, Caio J. C.
Tohoku Math. J. (2), Tome 52 (2000) no. 4, p. 271-282 / Harvested from Project Euclid
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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.
Publié le : 2000-05-14
Classification:  53D05,  32Q60,  53C15,  53C43,  53C55 
@article{1178224611,
     author = {Mo, Xiaohuan and Negreiros, Caio J. C.},
     title = {$(1,2)$-symplectic structures on flag manifolds},
     journal = {Tohoku Math. J. (2)},
     volume = {52},
     number = {4},
     year = {2000},
     pages = { 271-282},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1178224611}
}

Mo, Xiaohuan; Negreiros, Caio J. C. $(1,2)$-symplectic structures on flag manifolds. Tohoku Math. J. (2), Tome 52 (2000) no. 4, pp.  271-282. http://gdmltest.u-ga.fr/item/1178224611/