{
  "id": "1209.0857",
  "version": "v1",
  "published": "2012-09-05T04:37:08.000Z",
  "updated": "2012-09-05T04:37:08.000Z",
  "title": "On a new class of Finsler metrics",
  "authors": [
    "Changtao Yu",
    "Hongmei Zhu"
  ],
  "comment": "16 pages",
  "journal": "Differential Geometry and its Applications 29 (2011) 244-254",
  "doi": "10.1016/j.difgeo.2010.12.009",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, the geometric meaning of (alpha,beta)-norms is made clear. On this basis, we introduce a new class of Finsler metrics called general (alpha,beta)-metrics, which are defined by a Riemannian metric and an 1-form. These metrics not only generalize original (alpha,beta)-metrics naturally, but also include some metrics structured by R. Bryant. The notion of general (alpha,beta)-metrics is one of the original ideas belongs to the first author(another one is beta-deformations intruduced in the paper \"Deformations and Hilbert's Fourth Problem\"). We believe that the researches on general (alpha,beta)-metrics will enrich Finsler geometry and the approaches offer references for further study. But it seems that the classical methods suitable for (alpha,beta)-metrics may not be suitable for them, the idea used in this paper, which is closely related to beta-deformations, is non-classical. Any communication or suggestion is welcome.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-05T04:37:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53B40",
      "53C60"
    ],
    "keywords": [
      "finsler metrics",
      "approaches offer references",
      "hilberts fourth problem",
      "enrich finsler geometry",
      "original ideas belongs"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.0857Y"
    }
  }
}