{
  "id": "2205.11892",
  "version": "v1",
  "published": "2022-05-24T08:24:38.000Z",
  "updated": "2022-05-24T08:24:38.000Z",
  "title": "On Sprays of Scalar Curvature and Metrizability",
  "authors": [
    "Guojun Yang"
  ],
  "comment": "20 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "Every Finsler metric naturally induces a spray but not so for the converse. The notion for sprays of scalar (resp. isotropic) curvature has been known as a generalization for Finsler metrics of scalar (resp. isotropic) flag curvature. In this paper, a new notion, sprays of constant curvature, is introduced and especially it shows that a spray of isotropic curvature is not necessarily of constant curvature even in dimension $n\\ge3$. Further, complete conditions are given for sprays of isotropic (resp. constant) curvature to be Finsler-metrizabile. As applications of such a result, the local structure is determined for locally projectively flat Berwald sprays of isotropic (resp. constant) curvature which are Finsler-metrizable, and some more sprays of isotropic curvature are discussed for their metrizability. Besides, the metrizability problem is also investigated for sprays of scalar curvature under certain curvature conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-24T08:24:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C60",
      "53B40"
    ],
    "keywords": [
      "scalar curvature",
      "constant curvature",
      "isotropic curvature",
      "finsler metric",
      "locally projectively flat berwald sprays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}