"Darboux's theorem" meaning in English

{
  "etymology_text": "Named after Jean Gaston Darboux.",
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          "name": "Differential geometry",
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      "glosses": [
        "A theorem providing a normal form for special classes of differential 1-forms, partially generalizing the Frobenius integration theorem. One of its many consequences is that any two symplectic manifolds of the same dimension are locally symplectomorphic to one another."
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          "differential geometry",
          "differential geometry"
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          "normal form",
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          "differential",
          "differential"
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        [
          "symplectic",
          "symplectic"
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          "manifold",
          "manifold"
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          "dimension",
          "dimension"
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          "locally",
          "locally"
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        [
          "symplectomorphic",
          "symplectomorphic"
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      "qualifier": "differential geometry",
      "raw_glosses": [
        "(differential geometry) A theorem providing a normal form for special classes of differential 1-forms, partially generalizing the Frobenius integration theorem. One of its many consequences is that any two symplectic manifolds of the same dimension are locally symplectomorphic to one another."
      ]
    }
  ],
  "word": "Darboux's theorem"
}

{
  "etymology_text": "Named after Jean Gaston Darboux.",
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        "en:Differential geometry"
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      "glosses": [
        "A theorem providing a normal form for special classes of differential 1-forms, partially generalizing the Frobenius integration theorem. One of its many consequences is that any two symplectic manifolds of the same dimension are locally symplectomorphic to one another."
      ],
      "links": [
        [
          "differential geometry",
          "differential geometry"
        ],
        [
          "normal form",
          "normal form"
        ],
        [
          "differential",
          "differential"
        ],
        [
          "symplectic",
          "symplectic"
        ],
        [
          "manifold",
          "manifold"
        ],
        [
          "dimension",
          "dimension"
        ],
        [
          "locally",
          "locally"
        ],
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          "symplectomorphic",
          "symplectomorphic"
        ]
      ],
      "qualifier": "differential geometry",
      "raw_glosses": [
        "(differential geometry) A theorem providing a normal form for special classes of differential 1-forms, partially generalizing the Frobenius integration theorem. One of its many consequences is that any two symplectic manifolds of the same dimension are locally symplectomorphic to one another."
      ]
    }
  ],
  "word": "Darboux's theorem"
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