  We study the classification of special almost hermitian manifolds in Gray and
Hervella's type classes. We prove that the exterior derivatives of the
symplectic form and the complex volume form contain all the information about
the intrinsic torsion of the $\SUn(n)$-structure. Furthermore, we apply the
obtained results to almost hyperhermitian geometry. Thus, we show that the
exterior derivatives of the three K{\"a}hler forms of an almost hyperhermitian
manifold are sufficient to determine the three covariant derivatives of such
forms, i.e., the three mentioned exterior derivatives determine the intrinsic
torsion of the ${\sl Sp}(n)$-structure.

Differential Geometry