"Riemannian manifold" meaning in All languages combined

See Riemannian manifold on Wiktionary

Noun [English]

Forms: Riemannian manifolds [plural]
Etymology: Named after German mathematician Bernhard Riemann (1826–1866). See also Riemannian. Etymology templates: {{m|en|Riemannian}} Riemannian Head templates: {{en-noun}} Riemannian manifold (plural Riemannian manifolds)
  1. (differential geometry, Riemannian geometry) A real, smooth differentiable manifold whose each point has a tangent space equipped with a positive-definite inner product; Categories (topical): Differential geometry, Geometry
    Sense id: en-Riemannian_manifold-en-noun-E96wTJnC Disambiguation of Geometry: 50 50 Categories (other): English entries with incorrect language header, English entries with language name categories using raw markup, English terms with non-redundant non-automated sortkeys, Manifolds Disambiguation of English entries with incorrect language header: 45 55 Disambiguation of English entries with language name categories using raw markup: 45 55 Disambiguation of English terms with non-redundant non-automated sortkeys: 45 55 Disambiguation of Manifolds: 45 55
  2. (differential geometry, Riemannian geometry) A real, smooth differentiable manifold whose each point has a tangent space equipped with a positive-definite inner product; Categories (topical): Differential geometry, Geometry
    Sense id: en-Riemannian_manifold-en-noun-sH~I9sg3 Disambiguation of Geometry: 50 50 Categories (other): English entries with incorrect language header, English entries with language name categories using raw markup, English terms with non-redundant non-automated sortkeys, Manifolds Disambiguation of English entries with incorrect language header: 45 55 Disambiguation of English entries with language name categories using raw markup: 45 55 Disambiguation of English terms with non-redundant non-automated sortkeys: 45 55 Disambiguation of Manifolds: 45 55
The following are not (yet) sense-disambiguated
Synonyms: Riemannian space Hypernyms: differentiable manifold, smooth manifold Derived forms: pseudo-Riemannian manifold, semi-Riemannian manifold Related terms: differentiable manifold, Riemannian metric (alt: = Riemannian metric tensor) Translations (real, smooth differentiable manifold equipped with a Riemannian metric): variété riemannienne [feminine] (French), riemannsche Mannigfaltigkeit [feminine] (German), riemannscher Raum [masculine] (German), varietà riemanniana [feminine] (Italian), ри́маново многообра́зие (rímanovo mnogoobrázije) [neuter] (Russian)
Disambiguation of 'real, smooth differentiable manifold equipped with a Riemannian metric': 50 50

Inflected forms

Download JSON data for Riemannian manifold meaning in All languages combined (7.7kB)

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This page is a part of the kaikki.org machine-readable All languages combined 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.

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