Constant curvature

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.

[1] 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.

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