Loterre: Mathematics: Riemannian manifold

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

Riemannian manifold

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 g_p on the tangent space T_pM at each point p.
The family g_p 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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