On a remarkable class of paracontact metric manifolds

We study a remarkable class of paracontact metric manifolds which have no contact metric counterpart: the paracontact metric $(-1,\tilde{\mu })$-spaces which are not paraSasakian (i.e. have $\tilde{h}\mathrm{\ne }0$). We present explicit examples with $\tilde{h}$ of every possible constant rank and some with non-constant rank, which were not known to exist until recently.