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 $\star$-scalar curvature which satisfies the Kaehler condition at the point in question.
Miguel BROZOS-VÁZQUEZ. Peter GILKEY. Hyunsuk KANG. Stana NIKČEVIĆ. "Geometric realizations of Hermitian curvature models." J. Math. Soc. Japan 62 (3) 851 - 866, July, 2010. https://doi.org/10.2969/jmsj/06230851