"shape operator" meaning in English

{
  "forms": [
    {
      "form": "shape operators",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "shape operator (plural shape operators)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
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          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Differential geometry",
          "orig": "en:Differential geometry",
          "parents": [
            "Geometry",
            "Mathematical analysis",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Geometry",
          "orig": "en:Geometry",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1966, Barrett O'Neill, Elementary Differential Geometry, Academic Press, page 304",
          "text": "Gaussian curvature is a prime example; although defined in terms of shape operators, it belongs to this intrinsic geometry, since it passes the test of isometric invariance.",
          "type": "quotation"
        },
        {
          "ref": "2006, Balkan Journal of Geometry and Its Applications, volumes 11-12, page 41",
          "text": "Timelike surfaces have symmetric shape operators which can be put into one of three canonical forms on a fixed tangent space with respect to an orthonormal basis:[…].",
          "type": "quotation"
        },
        {
          "ref": "2007, John Oprea, Differential Geometry and Its Applications, Mathematical Association of America, page 85",
          "text": "We have already seen that a plane has zero shape operator. Intuitively, since the shape operator detects the change in the unit normal U, a zero shape operator for a surface M should imply that M is a plane. This is verified by the following result.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The differential of the Gauss map of an oriented surface at a given point on the surface."
      ],
      "id": "en-shape_operator-en-noun-ic9sdEFg",
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "differential geometry",
          "differential geometry"
        ],
        [
          "differential",
          "differential"
        ],
        [
          "Gauss map",
          "Gauss map"
        ],
        [
          "oriented",
          "oriented"
        ],
        [
          "surface",
          "surface"
        ]
      ],
      "qualifier": "differential geometry",
      "raw_glosses": [
        "(geometry, differential geometry) The differential of the Gauss map of an oriented surface at a given point on the surface."
      ],
      "synonyms": [
        {
          "sense": "differential of a Gauss map",
          "word": "Weingarten map"
        }
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "shape operator"
}

{
  "forms": [
    {
      "form": "shape operators",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "shape operator (plural shape operators)",
      "name": "en-noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "en:Differential geometry",
        "en:Geometry"
      ],
      "examples": [
        {
          "ref": "1966, Barrett O'Neill, Elementary Differential Geometry, Academic Press, page 304",
          "text": "Gaussian curvature is a prime example; although defined in terms of shape operators, it belongs to this intrinsic geometry, since it passes the test of isometric invariance.",
          "type": "quotation"
        },
        {
          "ref": "2006, Balkan Journal of Geometry and Its Applications, volumes 11-12, page 41",
          "text": "Timelike surfaces have symmetric shape operators which can be put into one of three canonical forms on a fixed tangent space with respect to an orthonormal basis:[…].",
          "type": "quotation"
        },
        {
          "ref": "2007, John Oprea, Differential Geometry and Its Applications, Mathematical Association of America, page 85",
          "text": "We have already seen that a plane has zero shape operator. Intuitively, since the shape operator detects the change in the unit normal U, a zero shape operator for a surface M should imply that M is a plane. This is verified by the following result.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The differential of the Gauss map of an oriented surface at a given point on the surface."
      ],
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "differential geometry",
          "differential geometry"
        ],
        [
          "differential",
          "differential"
        ],
        [
          "Gauss map",
          "Gauss map"
        ],
        [
          "oriented",
          "oriented"
        ],
        [
          "surface",
          "surface"
        ]
      ],
      "qualifier": "differential geometry",
      "raw_glosses": [
        "(geometry, differential geometry) The differential of the Gauss map of an oriented surface at a given point on the surface."
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "differential of a Gauss map",
      "word": "Weingarten map"
    }
  ],
  "word": "shape operator"
}