Constant curvature

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In mathematics, constant curvature is a concept from differential geometry. Here, curvature refers to the sectional curvature of a space (more precisely a manifold) and is a single number determining its local geometry. The sectional curvature is said to be constant if it has the same value at all points. For example, a sphere is a surface of constant positive curvature.

Classification[edit]

The Riemannian manifolds of constant curvature can be classified into the following three cases:

Properties[edit]