{
  "id": "2208.13694",
  "version": "v1",
  "published": "2022-08-29T16:11:42.000Z",
  "updated": "2022-08-29T16:11:42.000Z",
  "title": "The catenary in space forms",
  "authors": [
    "Rafael López"
  ],
  "comment": "2 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, the notion of the catenary curve in the sphere and in the hyperbolic plane is introduced. In both spaces, a catenary is defined as the shape of a hanging chain when its weight is measured with respect to a given geodesic of the space. Several characterizations of the catenary are established in terms of the curvature of the curve and of the angle that its unit normal makes with a vector field of the ambient space. Furthermore, in the hyperbolic plane, we extend the concept of catenary substituting the geodesics by a horocycle or the hyperbolic distance by the horocycle distance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-29T16:11:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A04",
      "53A10",
      "49J05"
    ],
    "keywords": [
      "space forms",
      "hyperbolic plane",
      "catenary curve",
      "horocycle distance",
      "ambient space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}