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2005 $f$-Structures on the classical flag manifold which admit (1,2)-symplectic metrics
Nir Cohen, Caio J. C. Negreiros, Marlio Paredes, Sofia Pinsón, Luiz A. B. San Martin
Tohoku Math. J. (2) 57(2): 261-271 (2005). DOI: 10.2748/tmj/1119888339


We characterize the invariant $f$-structures $\mathcal{F}$ on the classical maximal flag manifold $\mathbb F(n)$ which admit (1,2)-symplectic metrics. This provides a sufficient condition for the existence of $\mathcal{F}$-harmonic maps from any cosymplectic Riemannian manifold onto $\mathbb F(n)$. In the special case of almost complex structures, our analysis extends and unifies two previous approaches: a paper of Brouwer in 1980 on locally transitive digraphs, involving unpublished work by Cameron; and work by Mo, Paredes, Negreiros, Cohen and San Martin on cone-free digraphs. We also discuss the construction of (1,2)-symplectic metrics and calculate their dimension. Our approach is graph theoretic.


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Nir Cohen. Caio J. C. Negreiros. Marlio Paredes. Sofia Pinsón. Luiz A. B. San Martin. "$f$-Structures on the classical flag manifold which admit (1,2)-symplectic metrics." Tohoku Math. J. (2) 57 (2) 261 - 271, 2005.


Published: 2005
First available in Project Euclid: 27 June 2005

zbMATH: 1088.53018
MathSciNet: MR2137470
Digital Object Identifier: 10.2748/tmj/1119888339

Primary: 53C55
Secondary: 05C20‎, 17B45, 22F30

Rights: Copyright © 2005 Tohoku University


Vol.57 • No. 2 • 2005
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