{
  "id": "1605.01890",
  "version": "v1",
  "published": "2016-05-06T11:16:30.000Z",
  "updated": "2016-05-06T11:16:30.000Z",
  "title": "The Ricci tensor of almost parahermitian manifolds",
  "authors": [
    "Diego Conti",
    "Federico A. Rossi"
  ],
  "comment": "35 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study the pseudoriemannian geometry of almost parahermitian manifolds, obtaining a formula for the Ricci tensor of the Levi-Civita connection. The formula uses the intrinsic torsion of an underlying SL(n,R)-structure; we express it in terms of exterior derivatives of some appropriately defined differential forms. As an application, we construct Einstein and Ricci-flat examples on Lie groups. We disprove the parak\\\"ahler version of the Goldberg conjecture, and obtain the first compact examples of a non-flat, Ricci-flat nearly parak\\\"ahler structure. We study the paracomplex analogue of the first Chern class in complex geometry, which obstructs the existence of Ricci-flat parak\\\"ahler metrics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-06T11:16:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C15",
      "53C10",
      "53C29",
      "53C50"
    ],
    "keywords": [
      "parahermitian manifolds",
      "ricci tensor",
      "first compact examples",
      "levi-civita connection",
      "intrinsic torsion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}