{
  "id": "0903.0457",
  "version": "v1",
  "published": "2009-03-03T09:33:58.000Z",
  "updated": "2009-03-03T09:33:58.000Z",
  "title": "The classification of $δ$-homogeneous Riemannian manifolds with positive Euler characteristic",
  "authors": [
    "V. N. Berestovskii",
    "E. V. Nikitenko",
    "Yu. G. Nikonorov"
  ],
  "comment": "17 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "The authors give a short survey of previous results on $\\delta$-homogeneous Riemannian manifolds, forming a new proper subclass of geodesic orbit spaces with non-negative sectional curvature, which properly includes the class of all normal homogeneous Riemannian manifolds. As a continuation and an application of these results, they prove that the family of all compact simply connected indecomposable $\\delta$-homogeneous Riemannian manifolds with positive Euler characteristic, which are not normal homogeneous, consists exactly of all generalized flag manifolds $Sp(l)/U(1)\\cdot Sp(l-1)=\\mathbb{C}P^{2l-1}$, $l\\geq 2$, supplied with invariant Riemannian metrics of positive sectional curvature with the pinching constants (the ratio of the minimal sectional curvature to the maximal one) in the open interval $(1/16, 1/4)$. This implies very unusual geometric properties of the adjoint representation of $Sp(l)$, $l\\geq 2$. Some unsolved questions are suggested.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-03T09:33:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C25",
      "53C35"
    ],
    "keywords": [
      "positive euler characteristic",
      "classification",
      "geodesic orbit spaces",
      "normal homogeneous riemannian manifolds",
      "invariant riemannian metrics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.0457B"
    }
  }
}