{
  "id": "2112.07202",
  "version": "v2",
  "published": "2021-12-14T07:16:32.000Z",
  "updated": "2022-03-09T15:30:05.000Z",
  "title": "On the geometry of lift metrics and lift connections on the tangent bundle",
  "authors": [
    "Esmaeil Peyghan",
    "Davood Seifipour",
    "Adara M. Blaga"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We study lift metrics and lift connections on the tangent bundle $TM$ of a Riemannian manifold $(M,g)$. We also investigate the statistical and Codazzi couples of $TM$ and their consequences on the geometry of $M$. Finally, we prove a result on $1$-Stein and Osserman structures on $TM$, whenever $TM$ is equipped with the complete lift connection.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-03-09T15:30:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53B20",
      "53C05",
      "53C15",
      "53C25"
    ],
    "keywords": [
      "tangent bundle",
      "study lift metrics",
      "complete lift connection",
      "riemannian manifold",
      "codazzi couples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}