Tohoku Mathematical Journal
2000
June
SECOND SERIES VOL. 52, NO. 2

Tohoku Math. J.
52 (2000), 271-282

Title $(1, 2)$-SYMPLECTIC STRUCTURES ON FLAG MANIFOLDS

Author Xiaohuan Mo and Caio J. C. Negreiros

(Received October 9, 1998, revised June 14, 1999)
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.

1991 Mathematics Subject Classification. Primary 53C55; Secondary 58E20, 05C20.

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