{
  "id": "1805.04719",
  "version": "v1",
  "published": "2018-05-12T13:23:04.000Z",
  "updated": "2018-05-12T13:23:04.000Z",
  "title": "Lie Groups with flat Gauduchon connections",
  "authors": [
    "Luigi Vezzoni",
    "Bo Yang",
    "Fangyang Zheng"
  ],
  "comment": "8 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In \\cite{YZ-Gflat} it is considered the question of classifying compact Hermitian manifolds with flat $s$-Gauduchon connection, which is $\\nabla^s =(1-\\frac{s}{2})\\nabla^c + \\frac{s}{2}\\nabla^b$, where $\\nabla^c$ and $\\nabla^b$ are the Chern and Bismut connections respectively. In this note, we consider even-dimensional connected Lie group $G$ equipped with a left invariant metric $g$ and a compatible left invariant complex structure $J$. We show that when $s\\neq 0, 2$ and when there is a left invariant $\\nabla^s$-parallel frame, the manifold must be the flat K\\\"ahler space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-12T13:23:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "flat gauduchon connections",
      "compatible left invariant complex structure",
      "classifying compact hermitian manifolds",
      "left invariant metric",
      "even-dimensional connected lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}