See Riemannian geometry in All languages combined, or Wiktionary
Download JSON data for Riemannian geometry meaning in English (5.5kB)
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "Riemannian"
},
"expansion": "Riemannian",
"name": "m"
},
{
"args": {
"1": "en",
"2": "geometry"
},
"expansion": "geometry",
"name": "m"
}
],
"etymology_text": "From Riemannian + geometry, after German mathematician Bernhard Riemann.",
"forms": [
{
"form": "Riemannian geometries",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "-",
"2": "+"
},
"expansion": "Riemannian geometry (usually uncountable, plural Riemannian geometries)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Geometry",
"orig": "en:Geometry",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "92 8",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "88 12",
"kind": "other",
"name": "English entries with language name categories using raw markup",
"parents": [
"Entries with language name categories using raw markup",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "84 16",
"kind": "other",
"name": "English entries with topic categories using raw markup",
"parents": [
"Entries with topic categories using raw markup",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "89 11",
"kind": "other",
"name": "English terms with non-redundant non-automated sortkeys",
"parents": [
"Terms with non-redundant non-automated sortkeys",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "55 45",
"kind": "other",
"langcode": "en",
"name": "Non-Euclidean geometry",
"orig": "en:Non-Euclidean geometry",
"parents": [],
"source": "w+disamb"
}
],
"examples": [
{
"ref": "2001, Miklós Farkas, Dynamical Models in Biology, page 171",
"text": "Riemannian geometry was introduced by Riemann in 1854 as the n-dimensional generalization of the theory of curved surfaces of the 3D Euclidean space.",
"type": "quotation"
},
{
"ref": "2005, John F. Hawley, Katherine A. Holcomb, Foundations of Modern Cosmology, 2nd edition, page 235",
"text": "Such geometries are called Riemannian geometries; they are characterized by invariant distances (for example, the space-time interval) that depend at most on the squares of the coordinate distances (∆x or ∆t).",
"type": "quotation"
},
{
"ref": "2010, Saul Stahl, Geometry from Euclid to Knots, page 22",
"text": "Riemannian geometry has found many applications in science, the most spectacular of these being the theory of relativity.[…]Every Riemannian geometry has geodesics, which are defined as the shortest curves joining two points.",
"type": "quotation"
},
{
"ref": "2010, Ilka Agricola, “Chapter 9: Non-integrable geometries, torsion, and holonomy”, in Vicente Cortés, editor, Handbook of Pseudo-Riemannian Geometry and Supersymmetry, page 278",
"text": "At the beginning of the seventies, A. Gray generalized the classical holonomy concept by introducing a classification principle for non-integrable special Riemannian geometries [and] discovered in this context nearly Kähler manifolds in dimension six and nearly parallel G₂-manifolds in dimension seven.",
"type": "quotation"
},
{
"ref": "2013, Andrew McInerney, First Steps in Differential Geometry: Riemannian, Contact, Symplectic, page 195",
"text": "The concepts of Riemannian geometry are familiar: length, angle, distance, and curvature, among others. Historically tied to the origins of differential geometry, and with such familiar concepts, Riemannian geometry is often presented in textbooks as being synonymous with differential geometry itself, instead of as one differential-geometric structure among many.",
"type": "quotation"
}
],
"glosses": [
"The branch of differential geometry that concerns Riemannian manifolds; an example of a geometry that involves Riemannian manifolds."
],
"id": "en-Riemannian_geometry-en-noun-D4PjfafE",
"links": [
[
"mathematics",
"mathematics"
],
[
"geometry",
"geometry"
],
[
"differential geometry",
"differential geometry"
],
[
"Riemannian manifold",
"Riemannian manifold"
]
],
"raw_glosses": [
"(mathematics, geometry) The branch of differential geometry that concerns Riemannian manifolds; an example of a geometry that involves Riemannian manifolds."
],
"tags": [
"uncountable",
"usually"
],
"topics": [
"geometry",
"mathematics",
"sciences"
],
"translations": [
{
"_dis1": "78 22",
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "branch of differential geometry",
"word": "黎曼幾何"
},
{
"_dis1": "78 22",
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "límàn jǐhé",
"sense": "branch of differential geometry",
"word": "黎曼几何"
},
{
"_dis1": "78 22",
"code": "de",
"lang": "German",
"sense": "branch of differential geometry",
"tags": [
"feminine"
],
"word": "Riemannsche Geometrie"
},
{
"_dis1": "78 22",
"code": "ja",
"lang": "Japanese",
"sense": "branch of differential geometry",
"word": "リーマン幾何学"
}
]
},
{
"categories": [
{
"_dis": "55 45",
"kind": "other",
"langcode": "en",
"name": "Non-Euclidean geometry",
"orig": "en:Non-Euclidean geometry",
"parents": [],
"source": "w+disamb"
}
],
"glosses": [
"Elliptical or spherical geometry."
],
"id": "en-Riemannian_geometry-en-noun-ndl7mUEB",
"links": [
[
"Elliptical",
"elliptical"
],
[
"spherical",
"spherical geometry"
],
[
"geometry",
"geometry"
]
],
"tags": [
"uncountable",
"usually"
]
}
],
"wikipedia": [
"Bernhard Riemann",
"Riemannian geometry"
],
"word": "Riemannian geometry"
}
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English entries with language name categories using raw markup",
"English entries with topic categories using raw markup",
"English eponyms",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with non-redundant non-automated sortkeys",
"English uncountable nouns",
"en:Non-Euclidean geometry"
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "Riemannian"
},
"expansion": "Riemannian",
"name": "m"
},
{
"args": {
"1": "en",
"2": "geometry"
},
"expansion": "geometry",
"name": "m"
}
],
"etymology_text": "From Riemannian + geometry, after German mathematician Bernhard Riemann.",
"forms": [
{
"form": "Riemannian geometries",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "-",
"2": "+"
},
"expansion": "Riemannian geometry (usually uncountable, plural Riemannian geometries)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English terms with quotations",
"Quotation templates to be cleaned",
"en:Geometry",
"en:Mathematics"
],
"examples": [
{
"ref": "2001, Miklós Farkas, Dynamical Models in Biology, page 171",
"text": "Riemannian geometry was introduced by Riemann in 1854 as the n-dimensional generalization of the theory of curved surfaces of the 3D Euclidean space.",
"type": "quotation"
},
{
"ref": "2005, John F. Hawley, Katherine A. Holcomb, Foundations of Modern Cosmology, 2nd edition, page 235",
"text": "Such geometries are called Riemannian geometries; they are characterized by invariant distances (for example, the space-time interval) that depend at most on the squares of the coordinate distances (∆x or ∆t).",
"type": "quotation"
},
{
"ref": "2010, Saul Stahl, Geometry from Euclid to Knots, page 22",
"text": "Riemannian geometry has found many applications in science, the most spectacular of these being the theory of relativity.[…]Every Riemannian geometry has geodesics, which are defined as the shortest curves joining two points.",
"type": "quotation"
},
{
"ref": "2010, Ilka Agricola, “Chapter 9: Non-integrable geometries, torsion, and holonomy”, in Vicente Cortés, editor, Handbook of Pseudo-Riemannian Geometry and Supersymmetry, page 278",
"text": "At the beginning of the seventies, A. Gray generalized the classical holonomy concept by introducing a classification principle for non-integrable special Riemannian geometries [and] discovered in this context nearly Kähler manifolds in dimension six and nearly parallel G₂-manifolds in dimension seven.",
"type": "quotation"
},
{
"ref": "2013, Andrew McInerney, First Steps in Differential Geometry: Riemannian, Contact, Symplectic, page 195",
"text": "The concepts of Riemannian geometry are familiar: length, angle, distance, and curvature, among others. Historically tied to the origins of differential geometry, and with such familiar concepts, Riemannian geometry is often presented in textbooks as being synonymous with differential geometry itself, instead of as one differential-geometric structure among many.",
"type": "quotation"
}
],
"glosses": [
"The branch of differential geometry that concerns Riemannian manifolds; an example of a geometry that involves Riemannian manifolds."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"geometry",
"geometry"
],
[
"differential geometry",
"differential geometry"
],
[
"Riemannian manifold",
"Riemannian manifold"
]
],
"raw_glosses": [
"(mathematics, geometry) The branch of differential geometry that concerns Riemannian manifolds; an example of a geometry that involves Riemannian manifolds."
],
"tags": [
"uncountable",
"usually"
],
"topics": [
"geometry",
"mathematics",
"sciences"
]
},
{
"glosses": [
"Elliptical or spherical geometry."
],
"links": [
[
"Elliptical",
"elliptical"
],
[
"spherical",
"spherical geometry"
],
[
"geometry",
"geometry"
]
],
"tags": [
"uncountable",
"usually"
]
}
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "branch of differential geometry",
"word": "黎曼幾何"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "límàn jǐhé",
"sense": "branch of differential geometry",
"word": "黎曼几何"
},
{
"code": "de",
"lang": "German",
"sense": "branch of differential geometry",
"tags": [
"feminine"
],
"word": "Riemannsche Geometrie"
},
{
"code": "ja",
"lang": "Japanese",
"sense": "branch of differential geometry",
"word": "リーマン幾何学"
}
],
"wikipedia": [
"Bernhard Riemann",
"Riemannian geometry"
],
"word": "Riemannian 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.