Flat manifolds isospectral on p-forms

Zk 2-MANIFOLDS ARE ISOSPECTRAL ON FORMS.

Towers of isospectral manifolds

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 fibers isometric to the given ones and of basis any other given manifold. By iteration, we obtain families of isospectral not isometric manifolds.

Isospectral locally symmetric manifolds

In this article we construct closed, isospectral, non-isometric locally symmetric manifolds. We have three main results. First, we construct arbitrarily large sets of closed, isospectral, non-isometric manifolds. Second, we show the growth of size these sets of isospectral manifolds as a function of volume is super-polynomial. Finally, we construct pairs of infinite towers of finite covers of a...

On the Construction of Isospectral Riemannian Manifolds

Isospectral Conformal Metrics on 3 - Manifolds

Theorem. Let gj = u;go be a sequence of conformal metrics satisfying the following conditions. (i) Vol(M, g) = eto for some positive constant eto. (ii) f R2(g) + Ip(gj)1 2 dJj ::; et2 for some positive constant et2 where R(g) is the scalar curvature of gj and p is the Ricci tensor of gj and dJj = u~ dVO. (iii) Al (g), the lowest eigenvalue of the Laplacian of the metric gj' has a positive lower...