{
  "id": "2002.11558",
  "version": "v1",
  "published": "2020-02-26T15:18:46.000Z",
  "updated": "2020-02-26T15:18:46.000Z",
  "title": "Equigeodesics on generalized flag manifolds with $G_2$-type $t$-roots",
  "authors": [
    "Marina Statha"
  ],
  "comment": "14 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study homogeneous curves in generalized flag manifolds $G/K$ with $G_2$-type $t$-roots, which are geodesics with respect to each $G$-invariant metric on $G/K$. These curves are called equigeodesics. The tangent space of such flag manifolds splits into six isotropy summands, which are in one-to-one correspondence with $t$-roots. Also, these spaces are a generalization of the exceptional full flag manifold $G_2/T$. We give a characterization for structural equigeodesics for flag manifolds with $G_2$-type $t$-roots, and we give for each such flag manifold, a list of subspaces in which the vectors are structural equigeodesic vectors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-26T15:18:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25",
      "53C30",
      "13P10",
      "65H10",
      "68W30"
    ],
    "keywords": [
      "generalized flag manifolds",
      "exceptional full flag manifold",
      "structural equigeodesic vectors",
      "flag manifolds splits",
      "tangent space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}