"Gauss map" meaning in English

{
  "etymology_text": "Named after German mathematician Carl Friedrich Gauss.",
  "forms": [
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        "plural"
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  "lang_code": "en",
  "pos": "noun",
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          "kind": "topical",
          "langcode": "en",
          "name": "Differential geometry",
          "orig": "en:Differential geometry",
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          "kind": "topical",
          "langcode": "en",
          "name": "Geometry",
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Surfaces",
          "orig": "en:Surfaces",
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      "examples": [
        {
          "text": "1969 [Van Nostrand], Robert Osserman, A Survey of Minimal Surfaces, 2014, Dover, Unabridged republication, page 73,\nThere exist complete generalized minimal surfaces, not lying in a plane, whose Gauss map lies in an arbitrarily small neighborhood on the sphere."
        },
        {
          "text": "1985, R. G. Burns (translator), B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern Geometry― Methods and Applications: Part II: The Geometry and Topology of Manifolds, Springer, Graduate Texts in Mathematics, page 114,\n14.2.2 Theorem The integral of the Gaussian curvature over a closed hypersurface in Euclidean n-space is equal to the degree of the Gauss map of the surface, multiplied by γₙ (the Euclidean volume of the unit (n-1)-sphere)."
        },
        {
          "ref": "2005, F. L. Zak, Tangents and Secants of Algebraic Varieties, American Mathematical Society, page 5",
          "text": "In §2 we use results of §1 for the study of Gauss maps of projective varieties. The classical Gauss map associates to each point of a nonsingular real affine hypersurface the unit vector of the external normal at this point.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A map from a given oriented surface in Euclidean space to the unit sphere which maps each point on the surface to a unit vector orthogonal to the surface at that point."
      ],
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          "differential geometry",
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        [
          "surface",
          "surface"
        ],
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          "Euclidean space",
          "Euclidean space"
        ],
        [
          "unit sphere",
          "unit sphere"
        ],
        [
          "unit vector",
          "unit vector"
        ],
        [
          "orthogonal",
          "orthogonal"
        ]
      ],
      "qualifier": "differential geometry",
      "raw_glosses": [
        "(geometry, differential geometry) A map from a given oriented surface in Euclidean space to the unit sphere which maps each point on the surface to a unit vector orthogonal to the surface at that point."
      ],
      "related": [
        {
          "word": "shape operator"
        }
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
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      "wikipedia": [
        "Carl Friedrich Gauss",
        "Gauss map"
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  "word": "Gauss map"
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{
  "etymology_text": "Named after German mathematician Carl Friedrich Gauss.",
  "forms": [
    {
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      "tags": [
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  "lang_code": "en",
  "pos": "noun",
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      "examples": [
        {
          "text": "1969 [Van Nostrand], Robert Osserman, A Survey of Minimal Surfaces, 2014, Dover, Unabridged republication, page 73,\nThere exist complete generalized minimal surfaces, not lying in a plane, whose Gauss map lies in an arbitrarily small neighborhood on the sphere."
        },
        {
          "text": "1985, R. G. Burns (translator), B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern Geometry― Methods and Applications: Part II: The Geometry and Topology of Manifolds, Springer, Graduate Texts in Mathematics, page 114,\n14.2.2 Theorem The integral of the Gaussian curvature over a closed hypersurface in Euclidean n-space is equal to the degree of the Gauss map of the surface, multiplied by γₙ (the Euclidean volume of the unit (n-1)-sphere)."
        },
        {
          "ref": "2005, F. L. Zak, Tangents and Secants of Algebraic Varieties, American Mathematical Society, page 5",
          "text": "In §2 we use results of §1 for the study of Gauss maps of projective varieties. The classical Gauss map associates to each point of a nonsingular real affine hypersurface the unit vector of the external normal at this point.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A map from a given oriented surface in Euclidean space to the unit sphere which maps each point on the surface to a unit vector orthogonal to the surface at that point."
      ],
      "links": [
        [
          "geometry",
          "geometry"
        ],
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          "differential geometry",
          "differential geometry"
        ],
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        ],
        [
          "surface",
          "surface"
        ],
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          "Euclidean space",
          "Euclidean space"
        ],
        [
          "unit sphere",
          "unit sphere"
        ],
        [
          "unit vector",
          "unit vector"
        ],
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          "orthogonal",
          "orthogonal"
        ]
      ],
      "qualifier": "differential geometry",
      "raw_glosses": [
        "(geometry, differential geometry) A map from a given oriented surface in Euclidean space to the unit sphere which maps each point on the surface to a unit vector orthogonal to the surface at that point."
      ],
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        "geometry",
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