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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 an abstract and rigorous way to define it, now known as the curvature tensor. Similar notions have found applications everywhere in differential geometry.
For a more elementary discussion see the article on curvature which discusses the curvature of curves and surfaces in 2 and 3 dimensions, as well as the differential geometry of surfaces.
The curvature of a pseudo-Riemannian manifold can be expressed in the same way with only slight modifications.
== Ways to express the curvature of a Riemannian manifold ==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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