  We construct the first examples of continuous families of isospectral
Riemannian metrics that are not locally isometric on closed manifolds, more
precisely, on $S^n\times T^m$, where $T^m$ is a torus of dimension $m\ge 2$ and
$S^n$ is a sphere of dimension $n\ge 4$. These metrics are not locally
homogeneous; in particular, the scalar curvature of each metric is nonconstant.
For some of the deformations, the maximum scalar curvature changes during the
deformation.
