Smooth Rigidity for Higher-Dimensional Contact Anosov Flows

Andrey Gogolev, Federico Rodriguez Hertz

Research output: Contribution to journalArticlepeer-review

Abstract

We apply the technique of matching functions in the setting of contact Anosov flows satisfying a bunching assumption. This allows us to generalize the 3-dimensional rigidity result of Feldman and Ornstein [Ergodic Theory Dynam. Syst., 7, No. 1, 49–72 (1987)]. Namely, we show that if two Anosov flow of this kind are C0 conjugate, then they are Cr conjugate for some r ∈ [1, 2) or even C conjugate under certain additional assumptions. This, e.g., applies to geodesic flows on compact Riemannian manifolds of 1/4-pinched negative sectional curvature. We can also use our result to recover Hamendstädt’s marked length spectrum rigidity result for real hyperbolic manifolds.

Original languageEnglish (US)
Pages (from-to)1361-1370
Number of pages10
JournalUkrainian Mathematical Journal
Volume75
Issue number9
DOIs
StatePublished - Feb 2024

All Science Journal Classification (ASJC) codes

  • General Mathematics

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