Quantum ergodic restriction theorems, II: manifolds without boundary

This is the authors' abstract. We don't add key points for this paper.

We prove that if $(M, g)$ is a compact Riemannian manifold with ergodic geodesic flow, and if H ⊂ M is a smooth hypersurface satisfying a generic asymmetry condition with respect to the geodesic flow, then restrictions ϕⱼ |H of an orthonormal basis \ϕⱼ\ of $Δ$-eigenfunctions of $(M, g)$ to H are quantum ergodic on H. The condition on H is satisfied by geodesic circles, closed horocycles and generic closed geodesics on a hyperbolic surface.