Spectra of unit tangent bundles of compact hyperbolic Riemann surfaces (Q1264247)

Let \(S\) be a hyperbolic Riemann surface. Then both it and its unit tangent bundle \(T^1S\) are Riemannian manifolds. It has been known for a long time that two surfaces \(S_1,S_2\) are isospectral if and only if the length spectra coincide; this is a consequence of the Selberg trace formula. The authors shows here, using similar methods, that these also hold if the two corresponding properties hold for \(T^1S_1\) and \(T^S_2\).