Some results on the geometry of full flag manifolds and harmonic maps

In this note we study, for ? = 5,6,7, the geometry of the full flag manifolds, F(?) = U(?)/U(1)x⋅⋅⋅ x U(1).  By using tournaments we characterize all of the (1,2)-symplectic invariant metrics on F(?), for ? = 5,6,7, corresponding to different classes of non-integrable invariant almost complex structure.