{
  "id": "2205.10808",
  "version": "v1",
  "published": "2022-05-22T13:01:07.000Z",
  "updated": "2022-05-22T13:01:07.000Z",
  "title": "2-Ruled hypersurfaces in Minkowski 4-space and their constructions via octonions",
  "authors": [
    "Ameth Ndiaye",
    "Zehra Özdemir"
  ],
  "comment": "This is prepint paper which is submitted",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we define three types of 2-Ruled hypersurfaces in the Minkowski 4-space $\\mathbb{E}^4_1$. We obtain Gaussian and mean curvatures of the 2-ruled hypersurfaces of type-1 and type-2, and some characterizations about its minimality. We also deal with the first Laplace-Beltrami operators of these types of 2-Ruled hypersurfaces in $\\mathbb{E}^4_1$. Moreover, the importance of this paper is that the definition of these surfaces by using the octonions in $\\mathbb{E}^4_1$. Thus, this is a new idea and make the paper original. We give an example of 2-ruled hypersurface constructed by octonion and we visualize the projections of the images with MAPLE program. Furthermore, the optical fiber can be defined as a one-dimensional object embedded in the 4-dimensional Minkowski space $\\mathbb{E}^4_1$. Thus, as a discussion, we investigate the geometric evolution of a linearly polarized light wave along an optical fiber by means of the 2-ruled hypersurfaces in a four-dimensional Minkowski space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-22T13:01:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "53C42",
      "53C50",
      "53Z05",
      "53B50",
      "37C10",
      "57R25"
    ],
    "keywords": [
      "hypersurface",
      "constructions",
      "four-dimensional minkowski space",
      "first laplace-beltrami operators",
      "optical fiber"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}