{
  "id": "0905.1404",
  "version": "v1",
  "published": "2009-05-09T13:19:49.000Z",
  "updated": "2009-05-09T13:19:49.000Z",
  "title": "Time-like Salkowski and anti-Salkowski curves in Minkowski space $\\e_1^3$",
  "authors": [
    "Ahmad T Ali"
  ],
  "comment": "9 pages only",
  "categories": [
    "math.DG"
  ],
  "abstract": "Salkowski \\cite{salkow}, one century ago, introduced a family of curves with constant curvature but non-constant torsion (Salkowski curves) and a family of curves with constant torsion but non-constant curvature (anti-Salkowski curves) in Euclidean 3-space $\\e^3$. In this paper, we adapt definition of such curves to time-like curves in Minkowski 3-space $\\e_1^3$. Thereafter, we introduce an explicit parametrization of a time-like Salkowski curves and a time-like Anti-Salkowski curves in Minkowski space $\\e_1^3$. Also, we characterize them as space curve with constant curvature or constant torsion and whose normal vector makes a constant angle with a fixed line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-09T13:19:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C40",
      "53C50"
    ],
    "keywords": [
      "minkowski space",
      "non-constant curvature",
      "non-constant torsion",
      "adapt definition",
      "explicit parametrization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.1404A"
    }
  }
}