{
  "id": "2302.02543",
  "version": "v1",
  "published": "2023-02-06T03:01:12.000Z",
  "updated": "2023-02-06T03:01:12.000Z",
  "title": "Geometric structures in $Sol_3$",
  "authors": [
    "Siyao Liu"
  ],
  "comment": "35 pages. arXiv admin note: substantial text overlap with arXiv:2212.12243",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we conclude the geometric structures in $Sol_3$ with the Levi-Civita connection and the semi-symmetric non-metric connection. We discuss two special cases to study the geometric structures in $Sol_3$ with the semi-symmetric non-metric connection, namely $\\widehat{P}=a(X_3)\\partial_3$ and $\\widehat{P}=b(X_3)\\partial_1$, also get relatively complete conclusions respectively. As a special case, we investigate the geometric structures in $Sol_3$ with the Levi-Civita connection.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-06T03:01:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric structures",
      "semi-symmetric non-metric connection",
      "special case",
      "levi-civita connection",
      "relatively complete conclusions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}