On the classification of almost contact metric manifolds

On connected manifolds of dimension higher than three, the non-existence of $132$ Chinea and Gonz'alez-D'avila types of almost contact metric structures is proved. This is a consequence of some interrelations among components of the intrinsic torsion of an almost contact metric structure. Such interrelations allow to describe the exterior derivatives of some relevant forms in the context of almost contact metric geometry.