  We show that on an HKT manifold the holonomy of the Obata connection is
contained in SL(n,H) if and only if the Lee form is an exact one form. As an
application, we show compact HKT manifolds with holomorphically trivial
canonical bundle which are not balanced. A simple criterion for non-existence
of HKT metric on hypercomplex manifold is given in terms of the Ricci-type
tensors of the Obata connection.
