{
  "id": "1510.07989",
  "version": "v1",
  "published": "2015-10-26T15:35:00.000Z",
  "updated": "2015-10-26T15:35:00.000Z",
  "title": "Generalized P-Reducible $(α, β)$-Metrics with Vanishing S-curvature",
  "authors": [
    "A. Tayebi",
    "H. Sadeghi"
  ],
  "comment": "The main result holds for $(\\alpha, \\beta)$-Metrics with isotropic S-curvature!",
  "journal": "Annales Polonici Mathematici, 114(1) (2015), 67-79",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we study one of the open problems in Finsler geometry which presented by Matsumoto-Shimada about the existence of P-reducible metric which is not C-reducible. For this aim, we study a class of Finsler metrics called generalized P-reducible metrics that contains the class of P-reducible metrics. We prove that every generalized P-reducible $(\\alpha, \\beta)$-metric with vanishing S-curvature reduces to a Berwald metric or C-reducible metric. It results that there is not any concrete P-reducible $(\\alpha,\\beta)$-metric with vanishing S-curvature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-26T15:35:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C60",
      "53C25"
    ],
    "keywords": [
      "open problems",
      "berwald metric",
      "finsler geometry",
      "vanishing s-curvature reduces",
      "finsler metrics"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151007989T"
    }
  }
}