Constant curvature

See also: space form, curvature of Riemannian manifolds, and sectional curvature

In mathematics, constant curvature is a concept from differential geometry. Here, curvature refers to the sectional curvature of a space (more precisely a differentiable manifold) and is a single number that determines its local geometry. The sectional curvature is said to be constant if it has the same value at every point and for every two-dimensional tangent plane at that point. For example, a sphere is a surface of constant positive curvature.

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