{
  "id": "2208.14817",
  "version": "v1",
  "published": "2022-08-31T12:37:20.000Z",
  "updated": "2022-08-31T12:37:20.000Z",
  "title": "Integrable systems, Nijenhuis geometry and Lauricella bi-flat structures",
  "authors": [
    "Paolo Lorenzoni",
    "Sara Perletti"
  ],
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Combining the construction of integrable systems of hydrodynamic type starting from the Fr\\\"olicher-Nijenhuis bicomplex $(d,d_L)$ associated with a (1,1)-tensor field $L$ with vanishing Nijenhuis torsion with the construction of flat structures starting from integrable systems of hydrodynamic type we define multi-parameter families of bi-flat structures $(\\nabla,e,\\circ,\\nabla^*,*,E)$ associated with Fr\\\"olicher-Nijenhuis bicomplexes. We call these structures Lauricella bi-flat structures since in the n-dimensional semisimple case (n-1) flat coordinates of r are Lauricella functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-31T12:37:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integrable systems",
      "nijenhuis geometry",
      "hydrodynamic type",
      "structures lauricella bi-flat structures",
      "define multi-parameter families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}