{
  "annotation_id": "c7fd2293-f9b1-472c-aac5-9ea6d3627096",
  "date_created": "2026-02-17T05:53:04.781000Z",
  "date_modified": "2026-02-17T05:53:04.781000Z",
  "file_hash": "8d40c1d903d1e2dde3e910b88151514a016cc9dc52fcac5da1a8f8be242c1b5d",
  "private": false,
  "record": {
    "abstract": "There exists a complex structure $J$ on a connected open subset $S^3_{\\delta}\\times S^3$ of $S^6$. The present paper proves that: (1) $J$ can be extended to a global almost complex structure $\\widetilde{J}$ on $S^6$; (2) any extension to $S^6$ is necessarily non-integrable. Therefore, it is impossible to deform $\\widetilde{J}$ to an integrable almost complex structure on $S^6$ while fixing it on $S^3_{\\delta}\\times S^3$. This phenomenon indicates that the deformation strategy suggested by S.-T. Yau in his Problem 52 cannot be realized in this sense.",
    "arxiv_id": "2601.05568",
    "authors": [
      "Zizhou Tang",
      "Wenjiao Yan"
    ],
    "categories": [
      "math.CV",
      "math.AT",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Non-extendability of complex structures",
    "url": "https://arxiv.org/abs/2601.05568",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "67fb454a-4b39-498c-b9e6-c2aad5fef661",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}