  We prove that if $(M, g)$ is a compact Riemannian manifold with ergodic
geodesic flow, and if $H \subset M$ is a smooth hypersurface satisfying a
generic asymmetry condition with respect to the geodesic flow, then
restrictions $\phi_j |_H$ of an orthonormal basis $\{\phi_j\}$ of
$\Delta$-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.
