  We compute the condition of minimality of a G-structure for the Gray-Hervella
class $\mathcal{W}_4$ of almost hermitian manifolds and $\mathcal{C}_5$ class
of almost contact metric structures. We also consider $\mathcal{C}_4$ class by
comparison with the Grey-Hervella class $\mathcal{W}_4$. The common feature is
the existence of the Lee form $\theta$ representing these structures. We show
that these classes contain minimal G-structures. Here, minimality means
minimality of a $G$-structure inside oriented orthonormal frame bundle $SO(M)$
of a Riemannian manifold $M$.
