Abstract.
This paper considers invariant (1, 2)-symplectic almost Hermitian structures on the maximal flag manifod associated to a complex semi-simple Lie group G. The concept of cone-free invariant almost complex structure is introduced. It involves the rank-three subgroups of G, and generalizes the cone-free property for tournaments related to 𝕊l (n,ℂ) case. It is proved that the cone-free property is necessary for an invariant almost-complex structure to take part in an invariant (1, 2)-symplectic almost Hermitian structure. It is also sufficient if the Lie group is not B l , l ≥ 3, G 2 or F 4. For B l and F 4 a close condition turns out to be sufficient.
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Received: 28 October 2001
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Cohen, N., Negreiros, C. & San Martin, L. A rank-three condition for invariant (1, 2)-symplectic almost Hermitian structures on flag manifolds. Bull Braz Math Soc 33, 49–73 (2002). https://doi.org/10.1007/s005740200002
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DOI: https://doi.org/10.1007/s005740200002