Inverse spectral geometry of toroidal warped products
Annette Simonsen
Abstract: In this paper we study a class of compact manifolds for which
it is possible to determine the geometry if one knows the spectrum of the
Laplace operator acting on functions at the manifold. We prove that two
toroidal warped products are isometric if they have the same spectrum
and satisfy some symmetry conditions. At the end of the paper we use
scattering theory to obtain a similar result for non-compact manifolds.
Keywords: Inverse spectral geometry, inverse scattering theory.
MS classification: 58F19, 81U40.