ISOSPECTRAL DEFORMATIONS OF CLOSED RIEMANNIAN-MANIFOLDS WITH DIFFERENT SCALAR CURVATURE

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 x T-m, where T-m is a torus of dimension m gre ater than or equal to 2 and S-n is a sphere of dimension n greater tha n or equal to 4. These metrics are not locally homogeneous; in particu lar, the scalar curvature of each metric is nonconstant. For some of t he deformations, the maximum scalar curvature changes during the defor mation.