{
  "id": "math/0210335",
  "version": "v1",
  "published": "2002-10-22T03:05:17.000Z",
  "updated": "2002-10-22T03:05:17.000Z",
  "title": "Invariant Measure and the Euler Characteristic of Projectively Flat Manifolds",
  "authors": [
    "Kyeonghee Jo",
    "Hyuk Kim"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we show that the Euler characteristic of an even dimensional closed projectively flat manifold is equal to the total measure which is induced from a probability Borel measure on RP^n invariant under the holonomy action, and then discuss its consequences and applications. As an application, we show that the Chern's conjecture is true for a closed affinely flat manifold whose holonomy group action permits an invariant probability Borel measure on RP^n; that is, such a closed affinly flat manifold has a vanishing Euler characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-22T03:05:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R20",
      "53C15"
    ],
    "keywords": [
      "euler characteristic",
      "invariant measure",
      "invariant probability borel measure",
      "holonomy group action permits",
      "dimensional closed projectively flat manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10335J"
    }
  }
}