Quasiconformality in the geodesic flow of negatively curved manifolds (Q1924207)

Let \(M\) be a closed negatively curved Riemannian manifold. The author uses Zimmer's cocycle reduction lemma to show that the geodesic flow of \(M\) is uniformly quasiconformal on the expanding horospheres if its action on the tangent spaces of the expanding horospheres is measurably irreducible. By deep results of Sullivan, Kanai, Besson, Courtois, Gallot this in turn implies that the curvature of \(M\) is constant. In other words, closed hyperbolic manifolds can be characterized by purely dynamical properties of their geodesic flows.