### Abstract

A compact Riemannian manifold of dimension less than 4 with a finite number of semi-lines attached to the manifold is considered. It is shown that there is a deep analogy between the scattering and spectral properties of Schrodinger operators for this hybrid manifold and those for the automorphic Laplacian on Riemann surfaces with cusps. As an application, a relation between the scattering amplitude for hybrid manifolds with underlying compact Riemann surfaces of constant negative curvature and the Selberg zeta-function for this surface is obtained.