Families of (1,2)-symplectic metrics on full flag manifolds

Abstract

We obtain new families of (1,2)-symplectic invariant metrics on the full complex flag manifolds F(n). For n≥5, we characterize n−3 different n-dimensional families of (1,2)-symplectic invariant metrics on F(n). Each of these families corresponds to a different class of nonintegrable invariant almost complex structures on F(n).