Smooth rigidity for higher-dimensional contact Anosov flows
UDC 515.12 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)]. Nam...
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| Datum: | 2023 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2023
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7253 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 515.12
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 $C^0$ conjugate, then they are $C^{r}$ conjugate for some $r\in[1,2)$ or even $C^\infty$ conjugate under certain additional assumptions. This, for example, applies to geodesic flows on compact Riemannian manifolds of $1/4$-pinched negative sectional curvature. We can also use our result to recover Hamendstўаdt's marked length spectrum rigidity result for real hyperbolic manifolds. |
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| DOI: | 10.3842/umzh.v75i9.7253 |