{
  "annotation_id": "6893faa6-06f0-4f83-b4dc-4cc43377282e",
  "date_created": "2026-03-02T18:02:51.453000Z",
  "date_modified": "2026-03-02T18:02:51.453000Z",
  "file_hash": "28158c114b7100e618468102181d2c31a14d3f31379e0218ea10d5ce009d782b",
  "private": false,
  "record": {
    "abstract": "In this paper we study hypercomplex manifolds in four dimensions. Rather than\nusing an approach based on differential forms, we develop a dual approach using\nvector fields. The condition on these vector fields may then be interpreted as\nLax equations, exhibiting the integrability properties of such manifolds. A\nnumber of different field equations for such hypercomplex manifolds are\nderived, one of which is in Cauchy-Kovaleskaya form which enables a formal\ngeneral solution to be given. Various other properties of the field equations\nand their solutions are studied, such as their symmetry properties and the\nassociated hierarchy of conservation laws.",
    "arxiv_id": "solv-int/9808019",
    "authors": [
      "J. D. E. Grant",
      "I. A. B. Strachan"
    ],
    "categories": [
      "solv-int",
      "hep-th",
      "nlin.SI"
    ],
    "doi": "10.1088/0951-7715/12/5/302",
    "journal_ref": "Nonlinearity 12 (1999) 1247",
    "title": "Hypercomplex Integrable Systems",
    "url": "https://arxiv.org/abs/solv-int/9808019"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bd20009a-86c4-4976-be8a-0cd7bc2d324a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}