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. 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.

Classification

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

Properties

This article is issued from Wikipedia - version of the Sunday, November 22, 2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.