Invariant distributions and holomorphic vector fields in paracontact geometry

Having as a model the metric contact case of V. Brınzanescu; R. Slobodeanu, we study two similar subjects in the paracontact (metric) geometry: Distributions that are invariant with respect to the structure endomorphism φ, the class of vector fields of holomorphic type. As examples we consider both the 3-dimensional case and the general dimensional case through a Heisenberg-type structure inspired also by contact geometry.