Smooth rigidity for higher dimensional contact Anosov flows

2022/06/13 by Gogolev, Andrey, Hertz, Federico Rodriguez
#Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.06449

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~\citeFO. Namely, we show that if two such Anosov flows are C⁰ conjugate then they are C^r, conjugate for some r∈[1,2) or even C^∞ 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.

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