Towers of isospectral manifolds

Abstract

Given two isospectral not isometric manifolds, we construct a new couple of such manifolds as the total spaces of two Riemannian submersions with totally geodesic fibres isometric to the given ones and of basis any other given manifold. By iteration, we obtain families of isospectral not isometric manifolds.

Keywords:

• spectral geometry
• isospectrality

AMS Subject Classifications:

• 58J50
• 58J53
• 35P99

Acknowledgements

The work was supported by MURST of Italy.