{
  "id": "2307.04609",
  "version": "v1",
  "published": "2023-07-10T14:52:17.000Z",
  "updated": "2023-07-10T14:52:17.000Z",
  "title": "Complex structures on the product of two Sasakian manifolds",
  "authors": [
    "Marchidanu Vlad"
  ],
  "categories": [
    "math.DG",
    "math.AG",
    "math.CV"
  ],
  "abstract": "A Sasakian manifold is a Riemannian manifold whose metric cone admits a certain K\\\"ahler structure which behaves well under homotheties. We show that the product of two compact Sasakian manifolds admits a family of complex structures indexed by a complex nonreal parameter, none of whose members admits any compatible locally conformally K\\\"ahler metrics if both Sasakian manifolds are of dimension greater than $1$. We compare this family with another family of complex structures which has been studied in the literature. We compute the Dolbeault cohomology groups of these products of compact Sasakian manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-10T14:52:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex structures",
      "compact sasakian manifolds admits",
      "complex nonreal parameter",
      "metric cone admits",
      "dolbeault cohomology groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}