{
  "id": "1902.02500",
  "version": "v1",
  "published": "2019-02-07T07:26:11.000Z",
  "updated": "2019-02-07T07:26:11.000Z",
  "title": "Spectral properties of Killing vector fields of constant length",
  "authors": [
    "Yu. G. Nikonorov"
  ],
  "comment": "10 pages, comments are welcome",
  "categories": [
    "math.DG"
  ],
  "abstract": "This paper is devoted to the study of properties of Killing vector fields of constant length on Riemannian manifolds. If $\\mathfrak{g}$ is a Lie algebra of Killing vector fields on a given Riemannian manifold $(M,g)$, and $X\\in \\mathfrak{g}$ has constant length on $(M,g)$, then we prove that the linear operator $\\operatorname{ad}(X):\\mathfrak{g} \\rightarrow \\mathfrak{g}$ has a pure imaginary spectrum. More detailed structure results on the corresponding operator $\\operatorname{ad}(X)$ are obtained. Some special examples of vector fields of constant length are constructed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-07T07:26:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C25",
      "53C30"
    ],
    "keywords": [
      "killing vector fields",
      "constant length",
      "spectral properties",
      "riemannian manifold",
      "pure imaginary spectrum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}