  The space of the structure (0,3)-tensors of the covariant derivatives of the
structure endomorphism and the metric on almost contact B-metric manifolds is
considered. A known decomposition of this space in orthogonal and invariant
subspaces with respect to the action of the structure group is used. We
determine the corresponding components of the structure tensor and consider the
case of the lowest dimension 3 of the studied manifolds. Some examples are
commented.
