Almost Hermitian Geometry on Six Dimensional Nilmanifolds
  The fundamental 2-form of an invariant almost Hermitian structure on a 6-dimensional Lie group is described in terms of an action by SO(4)xU(1) on complex projective 3-space. This leads to a combinatorial description of the classes of almost Hermitian structures on the Iwasawa and other nilmanifolds. 
E. Abbena, S. Garbiero, S. Salamon