  Let (M, g) be a closed Riemannian manifold and gE the Euclidean metric. We
show that for m > 1, (M x R^m, (g + gE)) is not conformal to a positive
Einstein manifold. Moreover, (M x R^m, (g + gE)) is not conformal to a
Riemannian manifold of positive Ricci curvature, through a smooth, radial,
positive, integrable function of R^m, for m > 1. These results are motivated by
some recent questions on Yamabe constants.
