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topology > algebraic topology > manifold > differentiable manifold > Riemannian manifold
geometry > topological space > manifold > differentiable manifold > Riemannian manifold
geometry > differential geometry > differentiable manifold > Riemannian manifold
topology > differential topology > differentiable manifold > Riemannian manifold
geometry > differential geometry > Riemannian geometry > Riemannian manifold

Preferred term

Riemannian manifold  

Definition

  • In differential geometry, a Riemannian manifold or Riemannian space (M, g), so called after the German mathematician Bernhard Riemann, is a real, smooth manifold M equipped with a positive-definite inner product gp on the tangent space TpM at each point p.
    The family gp of inner products is called a Riemannian metric (or Riemannian metric tensor). Riemannian geometry is the study of Riemannian manifolds.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Riemannian_manifold)

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http://data.loterre.fr/ark:/67375/PSR-S78CS2MJ-M

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