Length equivalent hyperbolic manifolds

Length equivalent hyperbolic manifolds.

Chris Leininger, D. B. McReynolds, and Alan Reid

Two Riemannian manifolds are called length equivalent when the sets of lengths of closed geodesics (forgetting multiplicities) on the manifolds are equal. We give a construction of length equivalent Riemannian manifolds (that are non-isometric and non-isospectral) that works in some generality. For example we show that every finite volume hyperbolic n-manifold has an infinite family of pairs of length equivalent finite covers.