Geometric Realizations of Hermitian curvature models
  We show that a Hermitian algebraic curvature model satisfies the Gray identity if and only if it is geometrically realizable by a Hermitian manifold. Furthermore, such a curvature model can in fact be realized by a Hermitian manifold of constant scalar curvature and constant *-scalar curvature which satisfies the Kaehler condition at the point in question. 
M. Brozos-Vazquez, P. Gilkey, H. Kang, and S. Nikcevic