{
  "id": "1709.01399",
  "version": "v1",
  "published": "2017-09-02T11:56:56.000Z",
  "updated": "2017-09-02T11:56:56.000Z",
  "title": "Some topics in differential geometry of normed spaces",
  "authors": [
    "Vitor Balestro",
    "Horst Martini",
    "Ralph Teixeira"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1707.04226",
  "categories": [
    "math.DG"
  ],
  "abstract": "For a surface immersed in a three-dimensional space endowed with a norm instead of an inner product, one can define analogous concepts of curvature and metric. With these concepts in mind, various questions immediately appear. The aim of this paper is to propose and answer some of those questions. In this framework we prove several characterizations of minimal surfaces, and analogues of some global theorems (e.g., Hadamard-type theorems) are also derived. A result on the curvature of surfaces of constant Minkowski width is also given. Finally, we study the ambient metric induced on the surface, proving an extension of the classical Bonnet theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-02T11:56:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "differential geometry",
      "normed spaces",
      "constant minkowski width",
      "three-dimensional space",
      "minimal surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}