Curvature of Riemannian manifolds

In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension at least 3 is too complicated to be described by a single number at a given point. Riemann introduced a way to describe it as a "little monster tensor". Similar notions have found applications everywhere in differential geometry.

Related Topics:
Mathematics - Differential geometry - Riemannian manifold - Riemann - Tensor

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For a more elementary discussion see the article on curvature which discusses the curvature of curves and surfaces in 2 and 3 dimensions.

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The curvature of a Pseudo-Riemannian manifold can be expressed in the same way with only slight modifications.

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