{
  "id": "1905.03367",
  "version": "v1",
  "published": "2019-05-08T22:02:46.000Z",
  "updated": "2019-05-08T22:02:46.000Z",
  "title": "Fundamental theorem of spacelike curves in Lorentz-Minkowski space",
  "authors": [
    "Atsufumi Honda"
  ],
  "comment": "10 pages, no figure",
  "categories": [
    "math.DG"
  ],
  "abstract": "In Lorentz-Minkowski 3-space, the fundamental theorem of spacelike curves is known, if they have spacelike, timelike or lightlike curvature vector fields. However, such a theory cannot be applied to spacelike curves with type-changing curvature vector field. To fill the gap, in this paper, we introduce the pseudo-torsion functions along spacelike curves whose curvature vector field has isolated lightlike points, and prove the fundamental theorem for them. As an application, we obtain a necessary and sufficient condition for real analytic spacelike curves to be planar.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-08T22:02:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53B30",
      "57R45",
      "53A35"
    ],
    "keywords": [
      "fundamental theorem",
      "lorentz-minkowski space",
      "real analytic spacelike curves",
      "lightlike curvature vector fields",
      "type-changing curvature vector field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}