{
  "id": "2505.06631",
  "version": "v1",
  "published": "2025-05-10T12:43:46.000Z",
  "updated": "2025-05-10T12:43:46.000Z",
  "title": "Non-existence of cohomogeneity one Einstein metrics of two summands",
  "authors": [
    "Hanci Chi"
  ],
  "comment": "This submission contains the non-existence result originally part of arXiv:2405.10836v3, now split off for clarity. We appreciate the valuable feedback from our readers",
  "categories": [
    "math.DG"
  ],
  "abstract": "We prove the non-existence of cohomogeneity one Einstein metrics on a class of compact manifolds arising as double disk bundles, whose principal orbits split into two inequivalent irreducible summands. The proof uses a phase space barrier argument that yields a new obstruction to the existence of closed cohomogeneity one Einstein metrics, even when the principal orbits admit homogeneous Einstein metrics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-10T12:43:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25"
    ],
    "keywords": [
      "cohomogeneity",
      "non-existence",
      "orbits admit homogeneous einstein metrics",
      "principal orbits admit homogeneous einstein",
      "phase space barrier argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}