{
  "id": "1601.05231",
  "version": "v1",
  "published": "2016-01-20T10:40:02.000Z",
  "updated": "2016-01-20T10:40:02.000Z",
  "title": "Distinguished connections on $(J^{2}=\\pm 1)$-metric manifolds",
  "authors": [
    "Fernando Etayo",
    "Rafael Santamaría"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We study several linear connections (the first canonical, the Chern, the well adapted, the Levi Civita, the Kobayashi-Nomizu, the Yano, the Bismut and those with totally skew-symmetric torsion) which can be defined on the four geometric types of $(J^2=\\pm1)$-metric manifolds. We characterize when such a connection is adapted to the structure, and obtain a lot of results about coincidence among connections. We prove that the first canonical and the well adapted connections define a one-parameter family of adapted connections, named canonical connections, thus extending to almost Norden and almost product Riemannian manifolds the families introduced in almost Hermitian and almost para-Hermitian manifolds. We also prove that every connection studied in this paper is a canonical connection, when it exists and it is an adapted connection.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-20T10:40:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C15",
      "53C05",
      "53C50",
      "53C07"
    ],
    "keywords": [
      "metric manifolds",
      "distinguished connections",
      "canonical connection",
      "product riemannian manifolds",
      "levi civita"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}