Conditional measure and flip invariance of Bowen-Margulis and harmonic measures on manifolds of negative curvature

摘要

Kifer and Lcdrappier have asked whether the harmonic measures (vx) on manifolds of negative curvature arc equivalent to the conditional measures of the harmonic measure v of the geodesic flow associated with the h'bration (SxM)xeu- We settle this question with a rigidity result. We also clear up the same problem concerning the Patterson--Sullivan measure and the Bowen-Margulis measure.