{
  "annotation_id": "a9299df8-459a-4e33-b8d5-c7ed119791f5",
  "date_created": "2026-03-02T18:02:48.239000Z",
  "date_modified": "2026-03-02T18:02:48.239000Z",
  "file_hash": "6bc12aff20cbf15d8a78afdb35433858a0b5efcb00e894a0624c1e6a793cafe5",
  "private": false,
  "record": {
    "abstract": "We study the motion of surfaces in an intrinsic formulation in which the\nsurface is described by its metric and curvature tensors. The evolution\nequations for the six quantities contained in these tensors are reduced in\nnumber in two cases: (i) for arbitrary surfaces, we use principal coordinates\nto obtain two equations for the two principal curvatures, highlighting the\nsimilarity with the equations of motion of a plane curve; and (ii) for surfaces\nwith spatially constant negative curvature, we use parameterization by\nTchebyshev nets to reduce to a single evolution equation. We also obtain\nnecessary and sufficient conditions for a surface to maintain spatially\nconstant negative curvature as it moves. One choice for the surface\u0027s normal\nmotion leads to the modified-Korteweg de Vries equation,the appearance of which\nis explained by connections to the AKNS hierarchy and the motion of space\ncurves.",
    "arxiv_id": "solv-int/9306003",
    "authors": [
      "Robert I. McLachlan",
      "Harvey Segur"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "doi": "10.1016/0375-9601(94)91278-5",
    "title": "A note on the motion of surfaces",
    "url": "https://arxiv.org/abs/solv-int/9306003"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "75df770a-95ce-45b3-a3ef-fdb3ea686341",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}