{
  "id": "2505.05884",
  "version": "v1",
  "published": "2025-05-09T08:53:08.000Z",
  "updated": "2025-05-09T08:53:08.000Z",
  "title": "Local rigidity of group actions of isometries on compact Riemannian manifolds",
  "authors": [
    "Laurent Stolovitch",
    "Zhiyan Zhao"
  ],
  "comment": "In this work, we obtain rigidity results in both smooth and analytic cases. In the analytic case, we obtain some of the results of previous work arXiv:2312.07045 but we present here completely new proofs",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this article, we consider perturbations of isometries on a compact Riemannian manifold $M$. We investigate the smooth (resp. analytic) rigidity phenomenon of groups of these isometries. As a particular case, we prove that if a finite family of smooth (resp. analytic) small enough perturbations is simultaneously conjugate to the family of isometries via a finitely smooth diffeomorphism, then it is simultaneously smoothly (resp. analytically) conjugate to it whenever the family of isometries satisfies a Diophantine condition. Our results generalize the rigidity theorems of Arnold, Herman, Yoccoz, Moser, etc. about circle diffeomorphisms which are small perturbations of rotations as well as Fisher-Margulis's theorem on group actions satisfying Kazhdan's property (T).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-09T08:53:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compact riemannian manifold",
      "isometries",
      "local rigidity",
      "group actions satisfying kazhdans property",
      "perturbations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}