Ergodicity of unipotent flows and Kleinian groups

Abstract

Let M \mathcal {M} be a non-elementary convex cocompact hyperbolic 3 3 -manifold and δ \delta be the critical exponent of its fundamental group. We prove that a one-dimensional unipotent flow for the frame bundle of M \mathcal {M} is ergodic for the Burger-Roblin measure if and only if δ > 1 \delta >1 .