See Riemannian geometry in All languages combined, or Wiktionary
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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": "quote" }, { "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": "quote" }, { "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": "quote" }, { "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": "quote" } ], "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": "86 14", "code": "cmn", "lang": "Chinese Mandarin", "roman": "límàn jǐhé", "sense": "branch of differential geometry", "word": "黎曼幾何 /黎曼几何" }, { "_dis1": "86 14", "code": "de", "lang": "German", "sense": "branch of differential geometry", "tags": [ "feminine" ], "word": "Riemannsche Geometrie" }, { "_dis1": "86 14", "code": "ja", "lang": "Japanese", "sense": "branch of differential geometry", "word": "リーマン幾何学" } ] }, { "categories": [ { "_dis": "52 48", "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" }
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2025-03-01 from the enwiktionary dump dated 2025-02-21 using wiktextract (7c21d10 and f2e72e5). 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.
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