{
  "id": "1909.08119",
  "version": "v1",
  "published": "2019-09-17T21:46:41.000Z",
  "updated": "2019-09-17T21:46:41.000Z",
  "title": "The Mean Curvature of First-Order Submanifolds in Exceptional Geometries with Torsion",
  "authors": [
    "Gavin Ball",
    "Jesse Madnick"
  ],
  "comment": "37 pages. Section 2 of this preprint contains material from version 1 of our preprint arXiv:1905.03713. A new version of that preprint (1905.03713) will appear shortly to remove overlap",
  "categories": [
    "math.DG"
  ],
  "abstract": "We derive formulas for the mean curvature of associative 3-folds, coassociative 4-folds, and Cayley 4-folds in the general case where the ambient space has intrinsic torsion. Consequently, we are able to characterize those G2-structures (resp., Spin(7)-structures) for which every associative 3-fold (resp. coassociative 4-fold, Cayley 4-fold) is a minimal submanifold. In the process, we obtain new obstructions to the local existence of coassociative 4-folds in G2-structures with torsion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-17T21:46:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean curvature",
      "first-order submanifolds",
      "exceptional geometries",
      "ambient space",
      "intrinsic torsion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}