{
  "id": "1409.5968",
  "version": "v1",
  "published": "2014-09-21T11:11:52.000Z",
  "updated": "2014-09-21T11:11:52.000Z",
  "title": "Classification of Holomorphic Mappings of Hyperquadrics from $\\mathbb C^2$ to $\\mathbb C^3$",
  "authors": [
    "Michael Reiter"
  ],
  "comment": "35 pages",
  "categories": [
    "math.CV"
  ],
  "abstract": "We give a new proof of Faran's and Lebl's results by means of a new CR-geometric approach and classify all holomorphic mappings from the sphere in $\\mathbb C^2$ to Levi-nondegenerate hyperquadrics in $\\mathbb C^3$. We use the tools developed by Lamel, which allow us to isolate and study the most interesting class of holomorphic mappings. This family of so-called nondegenerate and transversal maps we denote by $\\mathcal F$. For $\\mathcal F$ we introduce a subclass $\\mathcal N$ of maps which are normalized with respect to the group $\\mathcal G$ of automorphisms fixing a given point. With the techniques introduced by Baouendi--Ebenfelt--Rothschild and Lamel we classify all maps in $\\mathcal N$. This intermediate result is crucial to obtain a complete classification of $\\mathcal F$ by considering the transitive part of the automorphism group of the hyperquadrics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-21T11:11:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32H02",
      "32V30"
    ],
    "keywords": [
      "holomorphic mappings",
      "complete classification",
      "lebls results",
      "intermediate result",
      "cr-geometric approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.5968R"
    }
  }
}