Curvature of Riemannian manifolds

From left to right: a surface of negative Gaussian curvature (hyperboloid), a surface of zero Gaussian curvature (cylinder), and a surface of positive Gaussian curvature (sphere). In higher dimensions, a manifold may have different curvatures in different directions, described by the Riemann curvature tensor.

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.

单词	Riemann curvature
释义	Riemann curvature 英语百科 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.
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Riemann curvature

Curvature of Riemannian manifolds