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A real, smooth differentiable manifold whose each point has a tangent space equipped with a positive-definite inner product;
Definition source: English Wiktionary via Wiktextract
Qualifier: differential geometry; Riemannian geometry; differential geometry; Riemannian geometry
Examples
- By definition, a Riemannian manifold M has at each point p a tangent space T#95;pM equipped with a positive-definite inner product, g#95;p; information about these inner products is encoded in the Riemannian metric tensor, g.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
A real, smooth differentiable manifold whose each point has a tangent space equipped with a positive-definite inner product; (more formally) an ordered pair (M, g), where M is a real, smooth differentiable manifold and g its Riemannian metric.
an ordered pair (M, g), where M is a real, smooth differentiable manifold and g its Riemannian metric.
Definition source: English Wiktionary via Wiktextract
Qualifier: differential geometry; Riemannian geometry; more formally
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Named after German mathematician Bernhard Riemann (1826–1866). See also Riemannian.
Across languages
Translations
8 source translations are retained for this English entry.
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Bulgarian:
риманово многообразие
(rimanovo mnogoobrazie)
— real, smooth differentiable manifold equipped with a Riemannian metric
-
French:
variété riemannienne
— real, smooth differentiable manifold equipped with a Riemannian metric
-
German:
riemannsche Mannigfaltigkeit
— real, smooth differentiable manifold equipped with a Riemannian metric
-
German:
riemannscher Raum
— real, smooth differentiable manifold equipped with a Riemannian metric
-
Italian:
varietà riemanniana
— real, smooth differentiable manifold equipped with a Riemannian metric
-
Polish:
rozmaitość riemannowska
— real, smooth differentiable manifold equipped with a Riemannian metric
-
Polish:
przestrzeń Riemanna
— real, smooth differentiable manifold equipped with a Riemannian metric
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Russian:
ри́маново многообра́зие
(rímanovo mnogoobrázije)
— real, smooth differentiable manifold equipped with a Riemannian metric
