"Riemannian manifold" meaning in English

See Riemannian manifold in All languages combined, or Wiktionary

Noun

Forms: Riemannian manifolds [plural]
Etymology: Named after German mathematician Bernhard Riemann (1826–1866). See also 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-pmZAmQRM Disambiguation of Geometry: 47 53 Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with French translations, Terms with German translations, Terms with Italian translations, Terms with Russian translations Disambiguation of English entries with incorrect language header: 48 52 Disambiguation of Entries with translation boxes: 48 52 Disambiguation of Pages with 1 entry: 47 53 Disambiguation of Pages with entries: 47 53 Disambiguation of Terms with French translations: 46 54 Disambiguation of Terms with German translations: 46 54 Disambiguation of Terms with Italian translations: 47 53 Disambiguation of Terms with Russian translations: 46 54
  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 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)
    Sense id: en-Riemannian_manifold-en-noun-sH~I9sg3 Disambiguation of Geometry: 47 53 Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with French translations, Terms with German translations, Terms with Italian translations, Terms with Russian translations, Manifolds Disambiguation of English entries with incorrect language header: 48 52 Disambiguation of Entries with translation boxes: 48 52 Disambiguation of Pages with 1 entry: 47 53 Disambiguation of Pages with entries: 47 53 Disambiguation of Terms with French translations: 46 54 Disambiguation of Terms with German translations: 46 54 Disambiguation of Terms with Italian translations: 47 53 Disambiguation of Terms with Russian translations: 46 54 Disambiguation of Manifolds: 39 61
The following are not (yet) sense-disambiguated
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': 47 53

Inflected forms

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          "text": "Further, a much harder theorem, due to J. Nash [31], says that a separable Riemannian manifold of dimension d can be isometrically embedded in #x5C;textstyle#x5C;mathbbRᴺ with N#x5C;le#x7B;#x5C;tfrac 1 2#x7D;d(d#x2B;1)(3d#x2B;11).",
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        "(differential geometry, Riemannian geometry) A real, smooth differentiable manifold whose each point has a tangent space equipped with a positive-definite inner product;"
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      "code": "fr",
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      "word": "variété riemannienne"
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      "word": "varietà riemanniana"
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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 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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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