  To what extent does the eigenvalue spectrum of the Laplace-Beltrami operator
on a compact Riemannian manifold determine the geometry of the manifold? We
give examples of isospectral manifolds with different local geometry including
continuous families of isospectral negatively curved manifolds with boundary as
well as various pairs of 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.
