  We show that if (X, f) is a locally connected Smale space such that the local
product structure on X can be lifted by a covering with virtually nilpotent
group of deck transformations to a global direct product, then (X, f) is
topologically conjugate to a hyperbolic infra-nilmanifold automorphism. We use
this result to give a generalization to Smale spaces of a theorem of M. Brin
and A. Manning on Anosov diffeomorphisms with pinched spectrum, and to show
that every locally connected codimension one Smale space is topologically
conjugate to a hyperbolic automorphism of a torus.
