{
  "id": "2206.06449",
  "version": "v1",
  "published": "2022-06-13T20:13:05.000Z",
  "updated": "2022-06-13T20:13:05.000Z",
  "title": "Smooth rigidity for higher dimensional contact Anosov flows",
  "authors": [
    "Andrey Gogolev",
    "Federico Rodriguez Hertz"
  ],
  "comment": "10 pages",
  "categories": [
    "math.DS",
    "math.DG"
  ],
  "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 Hamendst\\\"adt's marked length spectrum rigidity result for real hyperbolic manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-13T20:13:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "higher dimensional contact anosov flows",
      "smooth rigidity",
      "marked length spectrum rigidity result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}