{
  "id": "2008.10203",
  "version": "v1",
  "published": "2020-08-24T05:51:16.000Z",
  "updated": "2020-08-24T05:51:16.000Z",
  "title": "On a generalization of Monge--Ampère equations and Monge--Ampère systems",
  "authors": [
    "Masahiro Kawamata",
    "Kazuhiro Shibuya"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "We discuss Monge--Amp\\`ere equations from the view point of differential geometry. It is known that a Monge--Amp\\`ere equation corresponds to a special exterior differential system on a 1-jet space. In this paper, we generalize Monge--Amp\\`ere equations and prove that a $(k+1)$st order generalized Monge--Amp\\`ere equation corresponds to a special exterior differential system on a $k$-jet space. Then its solution naturally corresponds to an integral manifold of the corresponding exterior differential system. Moreover, we verify that the Korteweg-de Vries (KdV) equation and the Cauchy--Riemann equations are examples of our equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-24T05:51:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58A15",
      "58A17"
    ],
    "keywords": [
      "monge-ampère equations",
      "monge-ampère systems",
      "special exterior differential system",
      "generalization",
      "equation corresponds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}