{
  "id": "math/0609196",
  "version": "v2",
  "published": "2006-09-07T09:23:18.000Z",
  "updated": "2007-02-28T07:02:29.000Z",
  "title": "Hyperbolic Schwarz map for the hypergeometric differential equation",
  "authors": [
    "Takeshi Sasaki",
    "Kotaro Yamada",
    "Masaaki Yoshida"
  ],
  "comment": "16 pages, 8 figures",
  "categories": [
    "math.CA"
  ],
  "abstract": "The Schwarz map of the hypergeometric differential equation is studied since the beginning of the last century. Its target is the complex projective line, the 2-sphere. This paper introduces the hyperbolic Schwarz map, whose target is the hyperbolic 3-space. This map can be considered to be a lifting to the 3-space of the Schwarz map. This paper studies the singularities of this map, and visualize its image when the monodromy group is a finite group or a typical Fuchsian group. General cases will be treated in a forthcoming paper.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-02-28T07:02:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C05",
      "53C42"
    ],
    "keywords": [
      "hypergeometric differential equation",
      "hyperbolic schwarz map",
      "paper studies",
      "monodromy group",
      "complex projective line"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9196S"
    }
  }
}