{
  "id": "math/9908133",
  "version": "v2",
  "published": "1999-08-25T17:41:05.000Z",
  "updated": "1999-09-13T16:03:37.000Z",
  "title": "Almost invariant submanifolds for compact group actions",
  "authors": [
    "Alan Weinstein"
  ],
  "comment": "40 pages, minor corrections and additions",
  "categories": [
    "math.DG"
  ],
  "abstract": "We define a C^1 distance between submanifolds of a riemannian manifold M and show that, if a compact submanifold N is not moved too much under the isometric action of a compact group G, there is a G-invariant submanifold C^1-close to N. The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney's idea of realizing submanifolds as zeros of sections of extended normal bundles.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1999-09-13T16:03:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20"
    ],
    "keywords": [
      "compact group actions",
      "invariant submanifolds",
      "riemannian manifold",
      "averaging nearby submanifolds",
      "compact submanifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......8133W"
    }
  }
}