{
  "id": "1104.2664",
  "version": "v2",
  "published": "2011-04-14T04:38:26.000Z",
  "updated": "2011-04-28T14:37:16.000Z",
  "title": "Geodesic orbit manifolds and Killing fields of constant length",
  "authors": [
    "Yu. G. Nikonorov"
  ],
  "comment": "7 pages, some typos are corrected",
  "categories": [
    "math.DG"
  ],
  "abstract": "The goal of this paper is to clarify connections between Killing fields of constant length on a Rimannian geodesic orbit manifold $(M,g)$ and the structure of its full isometry group. The Lie algebra of the full isometry group of $(M,g)$ is identified with the Lie algebra of Killing fields $\\mathfrak{g}$ on $(M,g)$. We prove the following result: If $\\mathfrak{a}$ is an abelian ideal of $\\mathfrak{g}$, then every Killing field $X\\in \\mathfrak{a}$ has constant length. On the ground of this assertion we give a new proof of one result of C. Gordon: Every Riemannian geodesic orbit manifold of nonpositive Ricci curvature is a symmetric space.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-28T14:37:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C25",
      "53C35"
    ],
    "keywords": [
      "killing field",
      "constant length",
      "full isometry group",
      "rimannian geodesic orbit manifold",
      "lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.2664N"
    }
  }
}