{
  "id": "1402.6526",
  "version": "v4",
  "published": "2014-02-26T13:04:50.000Z",
  "updated": "2016-11-19T19:06:22.000Z",
  "title": "Integrability of geodesic flows for metrics on suborbits of the adjoint orbits of compact groups",
  "authors": [
    "Ihor V. Mykytyuk"
  ],
  "comment": "22 pages, Introduction is extended, some offprints are corrected",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $G/K$ be an orbit of the adjoint representation of a compact connected Lie group $G$, $\\sigma$ be an involutive automorphism of $G$ and $\\tilde G$ be the Lie group of fixed points of $\\sigma$. We find a sufficient condition for the complete integrability of the geodesic flow of the Riemannian metric on $\\tilde G/(\\tilde G\\cap K)$, which is induced by the bi-invariant Riemannian metric on $\\tilde G$. The integrals constructed here are real analytic functions, polynomial in momenta. It is checked that this sufficient condition holds when $G$ is the unitary group $U(n)$ and $\\sigma$ is its automorphism defined by the complex conjugation.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-14T09:46:35.000Z",
      "comment": "23 pages, Introduction is extended, Remark 2.19 and one reference are added, some offprints are corrected",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2016-11-19T19:06:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D25",
      "53D20",
      "22E60",
      "17B63"
    ],
    "keywords": [
      "geodesic flow",
      "adjoint orbits",
      "compact groups",
      "real analytic functions",
      "sufficient condition holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.6526M"
    }
  }
}