{
  "id": "0710.3668",
  "version": "v1",
  "published": "2007-10-19T10:13:23.000Z",
  "updated": "2007-10-19T10:13:23.000Z",
  "title": "Harmonic sections of tangent bundles equipped with Riemannian $g$-natural metrics",
  "authors": [
    "M. T. K. Abbassi",
    "G. Calvaruso",
    "D. Perrone"
  ],
  "comment": "27 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $(M,g)$ be a Riemannian manifold. When $M$ is compact and the tangent bundle $TM$ is equipped with the Sasaki metric $g^s$, the only vector fields which define harmonic maps from $(M,g)$ to $(TM,g^s)$, are the parallel ones. The Sasaki metric, and other well known Riemannian metrics on $TM$, are particular examples of $g$-natural metrics. We equip $TM$ with an arbitrary Riemannian $g$-natural metric $G$, and investigate the harmonicity of a vector field $V$ of $M$, thought as a map from $(M,g)$ to $(TM,G)$. We then apply this study to the Reeb vector field and, in particular, to Hopf vector fields on odd-dimensional spheres.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-19T10:13:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C43",
      "53C07",
      "53C15",
      "53D10"
    ],
    "keywords": [
      "natural metric",
      "tangent bundles",
      "harmonic sections",
      "sasaki metric",
      "define harmonic maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.3668A"
    }
  }
}