Canonical connections on paracontact manifolds

Abstract. The canonical paracontact connection is defined and it is shown that its torsion is the obstruction the paracontact manifold to be paraSasakian. A D-homothetic transformation is determined as a special gauge transformation. The η-Einstein manifold are defined, it is prove that their scalar curvature is a con-stant and it is shown that in the paraSasakian case these spaces can be obtained from Einstein paraSasakian manifolds with a D-homothetic transformations. It is shown that an almost paracontact structure admits a connection with totally skew-symmetric torsion if and only if the Nijenhuis tensor of the paracontact structure is skew-symmetric and the defining vector field is Killing