"differential geometry" meaning in English

See differential geometry in All languages combined, or Wiktionary

Noun

Forms: differential geometries [plural]
Head templates: {{en-noun|-|+}} differential geometry (usually uncountable, plural differential geometries)
  1. (geometry, mathematical analysis) The study of geometry, especially geometric structures on differentiable manifolds, using techniques from calculus, linear algebra and multilinear algebra. Wikipedia link: differential geometry Tags: uncountable, usually Categories (topical): Differential geometry, Geometry, Mathematical analysis Related terms: algebraic geometry, analytic geometry, projective geometry Translations (differential geometry): 微分幾何 (Chinese Mandarin), 微分几何 (wēifēn jǐhé) (Chinese Mandarin), differentiaaligeometria (Finnish), géométrie différentielle [feminine] (French), Differentialgeometrie [feminine] (German), Differenzialgeometrie [feminine] (German), differenciálgeometria (Hungarian), geometria differenziale [feminine] (Italian), 微分幾何学 (Japanese), диференција́лна геоме́трија (diferencijálna geométrija) [feminine] (Macedonian), geometria różniczkowa [feminine] (Polish), geometrie diferențială [feminine] (Romanian), дифференциальная геометрия (differencialʹnaja geometrija) [feminine] (Russian), diferencijalna geometrija [feminine] (Serbo-Croatian), geometría diferencial [feminine] (Spanish)
    Sense id: en-differential_geometry-en-noun-QJwXdb5r Categories (other): English entries with incorrect language header Topics: geometry, mathematical-analysis, mathematics, sciences

Inflected forms

Download JSON data for differential geometry meaning in English (5.1kB)

{
  "forms": [
    {
      "form": "differential geometries",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "-",
        "2": "+"
      },
      "expansion": "differential geometry (usually uncountable, plural differential geometries)",
      "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"
          ],
          "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"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "1945, Eric Temple Bell, The Development of Mathematics, 2nd Edition, 1992 Republication, page 358,\n[…] projective differential geometries of the American and Italian schools do not seem to have attracted physicists."
        },
        {
          "text": "1962, I. M. James, The Mathematical Works of J. H. C. Whitehead, Volume 1: Differential Geometry, page 189,\nThe general theory of manifolds of class 2 is a sub-class of differential geometries, which contain the theory of affine connections, curvature and osculating sub-spaces."
        },
        {
          "ref": "1993, M. A. Akivis, V. V. Goldberg, Projective Differential Geometry of Submanifolds, page v",
          "text": "Note that projective differential geometry is a basis for Euclidean and non-Euclidean differential geometries since metric properties of submanifolds of Euclidean and non-Euclidean spaces should only be added to their projective properties.",
          "type": "quotation"
        },
        {
          "ref": "2012, Heinrich W. Guggenheimer, Differential Geometry, page 145",
          "text": "In this sense, C#x7B;k#x5F;0#x7D; is the natural hypothesis of differentiability in the particular question of differential geometry.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The study of geometry, especially geometric structures on differentiable manifolds, using techniques from calculus, linear algebra and multilinear algebra."
      ],
      "id": "en-differential_geometry-en-noun-QJwXdb5r",
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "differentiable manifold",
          "differentiable manifold"
        ],
        [
          "calculus",
          "calculus"
        ],
        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "multilinear algebra",
          "multilinear algebra"
        ]
      ],
      "raw_glosses": [
        "(geometry, mathematical analysis) The study of geometry, especially geometric structures on differentiable manifolds, using techniques from calculus, linear algebra and multilinear algebra."
      ],
      "related": [
        {
          "word": "algebraic geometry"
        },
        {
          "word": "analytic geometry"
        },
        {
          "word": "projective geometry"
        }
      ],
      "tags": [
        "uncountable",
        "usually"
      ],
      "topics": [
        "geometry",
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "cmn",
          "lang": "Chinese Mandarin",
          "sense": "differential geometry",
          "word": "微分幾何"
        },
        {
          "code": "cmn",
          "lang": "Chinese Mandarin",
          "roman": "wēifēn jǐhé",
          "sense": "differential geometry",
          "word": "微分几何"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "differential geometry",
          "word": "differentiaaligeometria"
        },
        {
          "code": "fr",
          "lang": "French",
          "sense": "differential geometry",
          "tags": [
            "feminine"
          ],
          "word": "géométrie différentielle"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "differential geometry",
          "tags": [
            "feminine"
          ],
          "word": "Differentialgeometrie"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "differential geometry",
          "tags": [
            "feminine"
          ],
          "word": "Differenzialgeometrie"
        },
        {
          "code": "hu",
          "lang": "Hungarian",
          "sense": "differential geometry",
          "word": "differenciálgeometria"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "differential geometry",
          "tags": [
            "feminine"
          ],
          "word": "geometria differenziale"
        },
        {
          "code": "ja",
          "lang": "Japanese",
          "sense": "differential geometry",
          "word": "微分幾何学"
        },
        {
          "code": "mk",
          "lang": "Macedonian",
          "roman": "diferencijálna geométrija",
          "sense": "differential geometry",
          "tags": [
            "feminine"
          ],
          "word": "диференција́лна геоме́трија"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "differential geometry",
          "tags": [
            "feminine"
          ],
          "word": "geometria różniczkowa"
        },
        {
          "code": "ro",
          "lang": "Romanian",
          "sense": "differential geometry",
          "tags": [
            "feminine"
          ],
          "word": "geometrie diferențială"
        },
        {
          "code": "ru",
          "lang": "Russian",
          "roman": "differencialʹnaja geometrija",
          "sense": "differential geometry",
          "tags": [
            "feminine"
          ],
          "word": "дифференциальная геометрия"
        },
        {
          "code": "sh",
          "lang": "Serbo-Croatian",
          "sense": "differential geometry",
          "tags": [
            "feminine"
          ],
          "word": "diferencijalna geometrija"
        },
        {
          "code": "es",
          "lang": "Spanish",
          "sense": "differential geometry",
          "tags": [
            "feminine"
          ],
          "word": "geometría diferencial"
        }
      ],
      "wikipedia": [
        "differential geometry"
      ]
    }
  ],
  "word": "differential geometry"
}
{
  "forms": [
    {
      "form": "differential geometries",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "-",
        "2": "+"
      },
      "expansion": "differential geometry (usually uncountable, plural differential geometries)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "algebraic geometry"
    },
    {
      "word": "analytic geometry"
    },
    {
      "word": "projective geometry"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "English uncountable nouns",
        "en:Differential geometry",
        "en:Geometry",
        "en:Mathematical analysis"
      ],
      "examples": [
        {
          "text": "1945, Eric Temple Bell, The Development of Mathematics, 2nd Edition, 1992 Republication, page 358,\n[…] projective differential geometries of the American and Italian schools do not seem to have attracted physicists."
        },
        {
          "text": "1962, I. M. James, The Mathematical Works of J. H. C. Whitehead, Volume 1: Differential Geometry, page 189,\nThe general theory of manifolds of class 2 is a sub-class of differential geometries, which contain the theory of affine connections, curvature and osculating sub-spaces."
        },
        {
          "ref": "1993, M. A. Akivis, V. V. Goldberg, Projective Differential Geometry of Submanifolds, page v",
          "text": "Note that projective differential geometry is a basis for Euclidean and non-Euclidean differential geometries since metric properties of submanifolds of Euclidean and non-Euclidean spaces should only be added to their projective properties.",
          "type": "quotation"
        },
        {
          "ref": "2012, Heinrich W. Guggenheimer, Differential Geometry, page 145",
          "text": "In this sense, C#x7B;k#x5F;0#x7D; is the natural hypothesis of differentiability in the particular question of differential geometry.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The study of geometry, especially geometric structures on differentiable manifolds, using techniques from calculus, linear algebra and multilinear algebra."
      ],
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "differentiable manifold",
          "differentiable manifold"
        ],
        [
          "calculus",
          "calculus"
        ],
        [
          "linear algebra",
          "linear algebra"
        ],
        [
          "multilinear algebra",
          "multilinear algebra"
        ]
      ],
      "raw_glosses": [
        "(geometry, mathematical analysis) The study of geometry, especially geometric structures on differentiable manifolds, using techniques from calculus, linear algebra and multilinear algebra."
      ],
      "tags": [
        "uncountable",
        "usually"
      ],
      "topics": [
        "geometry",
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "differential geometry"
      ]
    }
  ],
  "translations": [
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "sense": "differential geometry",
      "word": "微分幾何"
    },
    {
      "code": "cmn",
      "lang": "Chinese Mandarin",
      "roman": "wēifēn jǐhé",
      "sense": "differential geometry",
      "word": "微分几何"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "differential geometry",
      "word": "differentiaaligeometria"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "differential geometry",
      "tags": [
        "feminine"
      ],
      "word": "géométrie différentielle"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "differential geometry",
      "tags": [
        "feminine"
      ],
      "word": "Differentialgeometrie"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "differential geometry",
      "tags": [
        "feminine"
      ],
      "word": "Differenzialgeometrie"
    },
    {
      "code": "hu",
      "lang": "Hungarian",
      "sense": "differential geometry",
      "word": "differenciálgeometria"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "differential geometry",
      "tags": [
        "feminine"
      ],
      "word": "geometria differenziale"
    },
    {
      "code": "ja",
      "lang": "Japanese",
      "sense": "differential geometry",
      "word": "微分幾何学"
    },
    {
      "code": "mk",
      "lang": "Macedonian",
      "roman": "diferencijálna geométrija",
      "sense": "differential geometry",
      "tags": [
        "feminine"
      ],
      "word": "диференција́лна геоме́трија"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "differential geometry",
      "tags": [
        "feminine"
      ],
      "word": "geometria różniczkowa"
    },
    {
      "code": "ro",
      "lang": "Romanian",
      "sense": "differential geometry",
      "tags": [
        "feminine"
      ],
      "word": "geometrie diferențială"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "differencialʹnaja geometrija",
      "sense": "differential geometry",
      "tags": [
        "feminine"
      ],
      "word": "дифференциальная геометрия"
    },
    {
      "code": "sh",
      "lang": "Serbo-Croatian",
      "sense": "differential geometry",
      "tags": [
        "feminine"
      ],
      "word": "diferencijalna geometrija"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "differential geometry",
      "tags": [
        "feminine"
      ],
      "word": "geometría diferencial"
    }
  ],
  "word": "differential geometry"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.