{
  "id": "1710.05535",
  "version": "v1",
  "published": "2017-10-16T06:49:46.000Z",
  "updated": "2017-10-16T06:49:46.000Z",
  "title": "Reductions of minimal Lagrangian submanifolds with symmetries",
  "authors": [
    "Toru Kajigaya"
  ],
  "comment": "22 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $M$ be a Fano manifold equipped with a K\\\"ahler form $\\omega\\in 2\\pi c_1(M)$ and $K$ a connected compact Lie group acting on $M$ as holomorphic isometries. In this paper, we show the minimality of a $K$-invariant Lagrangian submanifold $L$ in $M$ w.r.t. a globally conformal K\\\"ahler metric is equivalent to the minimality of the reduced Lagrangian submanifold $L_0=L/K$ in a K\\\"ahler quotient $M_0$ w.r.t. the Hsiang-Lawson metric. Furthermore, we give some examples of K\\\"ahler reductions by using a circle action obtained from a cohomogenenity one action on a K\\\"ahler-Einstein manifold of positive Ricci curvature. Applying these results, we obtain several examples of minimal Lagrangian submanifolds via reductions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-16T06:49:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D12",
      "53C42",
      "53D20"
    ],
    "keywords": [
      "minimal lagrangian submanifolds",
      "reductions",
      "symmetries",
      "invariant lagrangian submanifold",
      "ricci curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}