{
  "id": "math/0505579",
  "version": "v1",
  "published": "2005-05-26T17:47:10.000Z",
  "updated": "2005-05-26T17:47:10.000Z",
  "title": "On the Geometry of Classifying Spaces and Horizontal Slices",
  "authors": [
    "Zhiqin Lu"
  ],
  "journal": "Amer. J. Math, vol 121, 1999, pp 177-198",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we study the local properties of the moduli space of a polarized Calabi-Yau manifold. Let $U$ be a neighborhood of the moduli space. Then we know the universal covering space $V$ of $U$ is a smooth manifold. Suppose $D$ is the classifying space of a polarized Calabi-Yau manifold with the automorphism group $G$. Let $D_1$ be the symmetric space associated with $G$. Then we proved that the map from $V$ to $D_1$ induced by the period map is a pluriharmonic map. We also give a Kahler metric on $V$, which is called the Hodge metric. We proved that the Ricci curvature of the Hodge metric is negative away from zero. We also proved the non-existence of the K\\\"ahler metric on the classifying space of a Calabi-Yau threefold which is invariant under a cocompact lattice of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-05-26T17:47:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32G13",
      "58D27"
    ],
    "keywords": [
      "classifying space",
      "horizontal slices",
      "polarized calabi-yau manifold",
      "moduli space",
      "hodge metric"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5579L"
    }
  }
}