{
  "id": "2401.09024",
  "version": "v1",
  "published": "2024-01-17T07:38:39.000Z",
  "updated": "2024-01-17T07:38:39.000Z",
  "title": "Timelike Surfaces with Parallel Normalized Mean Curvature Vector Field in the Minkowski 4-Space",
  "authors": [
    "Victoria Bencheva",
    "Velichka Milousheva"
  ],
  "comment": "17 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In the present paper, we study timelike surfaces with parallel normalized mean curvature vector field in the four-dimensional Minkowski space. We introduce special isotropic parameters on each such surface, which we call canonical parameters, and prove a fundamental existence and uniqueness theorem stating that each timelike surface with parallel normalized mean curvature vector field is determined up to a rigid motion in the Minkowski space by three geometric functions satisfying a system of three partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, thus solving the Lund-Regge problem for this class of surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-17T07:38:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53B30",
      "53A35",
      "53B25"
    ],
    "keywords": [
      "parallel normalized mean curvature vector",
      "normalized mean curvature vector field",
      "timelike surface",
      "partial differential equations",
      "minkowski space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}