LAUSR

We prove that, on a generalized (multidimensional) Heisenberg group endowed with a left-invariant Sasakian structure, there exists a unique contact metric connection with skew torsion, invariant with respect to the group of automorphisms. The explicit expression of this connection in terms of the contact form and the metric tensor is obtained. It is shown that the torsion tensor and the curvature tensor are covariantly constant, and the sectional curvature varies between —1 and 0. It is proved that the obtained connection is a contact metric connection for any k-contact metric structure, therefore it is a contact metric connection for any Sasakian structure.