{
  "id": "1905.03713",
  "version": "v1",
  "published": "2019-05-09T15:50:11.000Z",
  "updated": "2019-05-09T15:50:11.000Z",
  "title": "The Mean Curvature of First-Order Submanifolds in Geometries with Torsion",
  "authors": [
    "Gavin Ball",
    "Jesse Madnick"
  ],
  "comment": "45 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We derive formulas for the mean curvature of special Lagrangian 3-folds, associative 3-folds, and coassociative 4-folds in the general case where the ambient space has intrinsic torsion. Consequently, we are able to characterize those SU(3)-structures (resp., G2-structures) for which every special Lagrangian 3-fold (resp. associative 3-fold, coassociative 4-fold) is a minimal submanifold. In the process, we obtain obstructions to the local existence of special Lagrangian 3-folds and coassociative 4-folds in manifolds with torsion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-09T15:50:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean curvature",
      "first-order submanifolds",
      "special lagrangian",
      "geometries",
      "ambient space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}