  We introduce the notion of paraquaternionic contact structures (pqc
structures), which turns out to be a generalization of the para 3-Sasakian
geometry. We derive a distinguished linear connection preserving the pqc
structure. Its torsion tensor is expressed explicitly in terms of the structure
tensors and the structure equations of a pqc manifold are presented. We define
pqc-Einstein manifolds and show that para 3-Sasakian spaces are precisely pqc
manifolds, which are pqc-Einstein. Furthermore, we introduce the
paraquaternionic Heisenberg qroup and show that it is the flat model of the pqc
geometry.
