Title: Conformal para quaternionic contact curvature and the local flatness theorem

Abstract: A tensor invariant is defined on a para quaternionic contact manifold in terms of the curvature and torsion of the canonical para quaternionic connection involving derivatives up to third order of the contact form. This tensor, called para quaternionic contact conformal curvature, is similar to the Weyl conformal curvature in Riemannian geometry, the Chern-Moser tensor in CR geometry, the para contact curvature in para CR geometry and to the quaternionic contact conformal curvature in quaternionic contact geometry.
It is shown that a para quaternionic contact manifold is locally para quaternionic contact conformal to the standard flat para quaternionic contact structure on the para quaternionic Heisenberg group, or equivalently, to the standard para 3-Sasakian structure on the para quaternionic pseudo-sphere iff the para quaternionic contact conformal curvature vanishes.