{
  "id": "1904.06533",
  "version": "v1",
  "published": "2019-04-13T12:34:33.000Z",
  "updated": "2019-04-13T12:34:33.000Z",
  "title": "Lichnerowicz-Obata Estimate, Almost Parallel $p$-form and Almost Product Manifolds",
  "authors": [
    "Masayuki Aino"
  ],
  "comment": "76 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We show a Lichnerowicz-Obata type estimate for the first eigenvalue of the Laplacian of $n$-dimensional closed Riemannian manifolds with an almost parallel $p$-form ($2\\leq p \\leq n/2$) in $L^2$-sense, and give a pinching result about the almost equality case when $2\\leq p<n/2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-13T12:34:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20"
    ],
    "keywords": [
      "product manifolds",
      "lichnerowicz-obata estimate",
      "lichnerowicz-obata type estimate",
      "dimensional closed riemannian manifolds",
      "first eigenvalue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 76,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}