To what extent does the eigenvalue spectrum of the Laplace-Beltrami
operator on a compact Riemannian manifold determine the geometry of
the manifold? We present a method for constructing isospectral
manifolds with different local geometry, generalizing an earlier
technique. Examples include continuous families of isospectral
negatively curved manifolds with boundary as well as various pairs of
isospectral manifolds. The latter illustrate that the spectrum does
not determine whether a manifold with boundary has negative curvature,
whether it has constant Ricci curvature, and whether it has parallel
curvature tensor, and the spectrum does not determine whether a closed
manifold has constant scalar curvature.