  A curvature-type tensor invariant called para contact (pc) conformal
curvature is defined on a paracontact manifold. It is shown that a paracontact
manifold is locally paracontact conformal to the hyperbolic Heisenberg group or
to a hyperquadric of neutral signature if and only if the pc conformal
curvature vanishes. In the three dimensional case the corresponding result is
achieved through employing a certain symmetric (0,2) tensor. The well known
result of Cartan-Chern-Moser giving necessary and sufficient condition a
CR-structure to be CR equivalent to a hyperquadric in the complex vector space
is presented in-line with the paracontact case. An explicit formula for the
regular part of a solution to the sub-ultrahyperbolic Yamabe equation on the
hyperbolic Heisenberg group is shown.
