{
  "id": "1412.1810",
  "version": "v1",
  "published": "2014-12-04T20:44:55.000Z",
  "updated": "2014-12-04T20:44:55.000Z",
  "title": "New progress in the inverse problem in the calculus of variations",
  "authors": [
    "Thoan Do",
    "Geoff Prince"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We present a new class solutions for the inverse problem in the calculus of variations in arbitrary dimension n. We also provide a number of new theorems concerning the inverse problem using exterior differential systems theory. Our new techniques provide a significant advance in the understanding of the inverse problem in arbitrary dimension. We show that when the eigenvalues of a certain curvature tensor are distinct and with n-1 integrable eigen-distributions, the corresponding differential equations are variational only if the non-integrable eigenspace has a certain geometric property. The resulting Lagrangians depend on n-1 functions each of 2 variables. We give some non-trivial examples in dimension 3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-04T20:44:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70H03",
      "53B05",
      "58A15",
      "37J05"
    ],
    "keywords": [
      "inverse problem",
      "variations",
      "arbitrary dimension",
      "exterior differential systems theory",
      "non-trivial examples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.1810D"
    }
  }
}