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Riemannian manifold

Riemannian manifold noun: a real, smooth differentiable manifold whose each point has a tangent space equipped with a positive-definite inner product;.

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;
    • 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.
    • In this chapter we extend the study of eigenvalues to Riemannian manifolds whose curvature may not be constant, but is, nevertheless, bounded.1984, Isaac Chavel, Eigenvalues in Riemannian Geometry, Academic Press, page 55
  2. (differential geometry, Riemannian geometry, more formally) an ordered pair (M, g), where M is a real, smooth differentiable manifold and g its Riemannian metric.
    Synonyms:
    Riemannian space

Synonyms of Riemannian manifold

  • Riemannian space

Forms of Riemannian manifold

pluralRiemannian manifolds

Origin of Riemannian manifold

Named after German mathematician Bernhard Riemann (1826–1866). See also Riemannian.

Words formed from Riemannian manifold

Questions about Riemannian manifold

What does Riemannian manifold mean?
Riemannian manifold means a real, smooth differentiable manifold whose each point has a tangent space equipped with a positive-definite inner product;.
What part of speech is Riemannian manifold?
Riemannian manifold is a noun.
What is the plural of Riemannian manifold?
The plural of Riemannian manifold is Riemannian manifolds.

Words near Riemannian manifold in the dictionary

  1. Riemann-Stieltjes integrals
  2. Riemannean
  3. riemannian
  4. Riemannian geometries
  5. Riemannian geometry
  6. Riemannian manifold
  7. Riemannian manifolds
  8. Riemannians
  9. Riemans
  10. Riemenschneider
  11. Riemenschneiders

Source and license

Adapted from Wiktionary: Riemannian manifold (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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