Cs. Gordon et al., ISOSPECTRAL DEFORMATIONS OF CLOSED RIEMANNIAN-MANIFOLDS WITH DIFFERENT SCALAR CURVATURE, Annales de l'Institut Fourier, 48(2), 1998, pp. 593
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.