{
  "id": "1404.2467",
  "version": "v1",
  "published": "2014-04-09T12:49:28.000Z",
  "updated": "2014-04-09T12:49:28.000Z",
  "title": "On minimal Legendrian submanifolds of Sasaki-Einstein manifolds",
  "authors": [
    "Simone Calamai",
    "David Petrecca"
  ],
  "comment": "14 pages. Comments and remarks are welcome",
  "categories": [
    "math.DG"
  ],
  "abstract": "For a given minimal Legendrian submanifold $L$ of a Sasaki-Einstein manifold we construct two families of eigenfunctions of the Laplacian of $L$ and we give a lower bound for the dimension of the corresponding eigenspace. Moreover, in the case the lower bound is attained, we prove that $L$ is totally geodesic and a rigidity result about the ambient manifold. This is a generalization of a result for the standard Sasakian sphere done by L\\^e and Wang.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-09T12:49:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C25",
      "53C42"
    ],
    "keywords": [
      "minimal legendrian submanifold",
      "sasaki-einstein manifold",
      "lower bound",
      "standard sasakian sphere",
      "rigidity result"
    ],
    "publication": {
      "doi": "10.1142/S0129167X14500839"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.2467C",
      "inspire": 1386198
    }
  }
}