Geometric realizations of Hermitian curvature models

Abstract

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.