Smooth rigidity for higher dimensional contact Anosov flows

Abstract

We apply the matching functions technique in the setting of contact Anosov flows which satisfy a bunching assumption. This allows us to generalize the 3-dimensional rigidity result of Feldman-Ornstein~\cite{FO}. Namely, we show that if two such Anosov flows are $C^0$ conjugate then they are $C^r$, conjugate for some $r\in [1,2)$ or even $C^{\infty }$ conjugate under some additional assumptions. This, for example, applies to $1/4$-pinched geodesic flows on compact Riemannian manifolds of negative sectional curvature. We can also use our result to recover Hamendstädt's marked length spectrum rigidity result for real hyperbolic manifolds.

10 pages, V2: improvements thanks to the referee report