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#curvature_of_riemannian_manifolds

Curvature of Riemannian manifolds

In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension greater than 2 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous way to define curvature for these manifolds, now known as the Riemann curvature tensor. Similar notions have found applications everywhere in differential geometry of surfaces and other objects. The curvature of a pseudo-Riemannian manifold can be expressed in the same way with only slight modifications.

Mon 19th

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Curvature of Riemannian manifolds Riemann curvature tensor Ricci curvature Riemannian manifold Curvature Sectional curvature Pseudo-Riemannian manifold Curvature form List of differential geometry topics Riemannian geometry
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