{
  "annotation_id": "5ee1326c-da83-4396-ae41-e590610b9376",
  "date_created": "2026-02-17T05:53:07.766000Z",
  "date_modified": "2026-02-17T05:53:07.766000Z",
  "file_hash": "dc08e2a0d258a634c5346b8a7dcd755c8df02f22103f56d44085e741db0f951f",
  "private": false,
  "record": {
    "abstract": "In this note, we study Einstein manifolds whose curvature operator of the second kind $\\mathring{R}$ satisfies the cone condition \\[ \\alpha^{-1}\\big(\\sum_{i=1}^{[\\alpha]} \\lambda_i+ (\\alpha - [\\alpha] ) \\lambda_{[\\alpha] + 1} \\big) \\ge -\\theta \\bar{\\lambda} \\] for some real number $\\alpha \\in [1, (n+2)(n-1)/2)$. Here $[\\alpha] :=\\max\\{ m \\in \\mathbb{Z}: m \\leq \\alpha\\}$, $\\theta\u003e-1$ and $\\lambda_1 \\le \\cdots \\le \\lambda_{(n+2)(n-1)/2}$ are the eigenvalues of $\\mathring{R}$ and $\\bar{\\lambda}$ is their average. The main result states that any closed Einstein manifold of dimension $n \\ge 4$ with $\\mathring{R}$ satisfies the cone condition is flat or a round sphere. These results generalize recent works corresponding to $\\alpha \\in \\mathbb Z_+$ of the authors \\cite{CW24-1,CW25-2} and Fu-Lu \\cite{FL25}.",
    "arxiv_id": "2601.06556",
    "authors": [
      "Haiqing Cheng",
      "Kui Wang"
    ],
    "categories": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Cone Conditions for the Curvature Operator of the Second Kind on Einstein Manifolds",
    "url": "https://arxiv.org/abs/2601.06556",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a793ed10-d9ee-487d-8100-815f6b6d2c41",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}