{
  "id": "1610.01474",
  "version": "v1",
  "published": "2016-10-05T15:13:38.000Z",
  "updated": "2016-10-05T15:13:38.000Z",
  "title": "Left Invariant Randers Metrics of Berwald type on Tangent Lie Groups",
  "authors": [
    "Farhad Asgari",
    "Hamid Reza Salimi Moghaddam"
  ],
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Let $G$ be a Lie group equipped with a left invariant Randers metric of Berward type $F$, with underlying left invariant Riemannian metric $g$. Suppose that $\\widetilde{F}$ and $\\widetilde{g}$ are lifted Randers and Riemannian metrics arising from $F$ and $g$ on the tangent Lie group $TG$ by vertical and complete lifts. In this article we study the relations between the flag curvature of the Randers manifold $(TG,\\widetilde{F})$ and the sectional curvature of the Riemannian manifold $(G,g)$ when $\\widetilde{F}$ is of Berwald type. Then we give all simply connected $3$-dimentional Lie groups such that their tangent bundles admit Randers metrics of Berwarld type and their geodesics vectors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-05T15:13:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "left invariant randers metric",
      "tangent lie group",
      "berwald type",
      "tangent bundles admit randers metrics",
      "riemannian metric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}