It is widely known that the spetrum fails to charaterise a Riemannian manifold. There are, however, Riemannian manifolds which admit no non-trivial continuous
isospetral deformations. Strongly expected to be a generic phenomenon, the absence of non-trivial isospectral deformations is referred to as spectral rigidity. The
present work treats two instances therof.

Keywords : Laplace-Beltrami Operstor, spectrum, isospectrality, isospectral deformations, quadratic forms.