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Constant curvature : ウィキペディア英語版
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:
* elliptic geometry – constant positive sectional curvature
* Euclidean geometry – constant vanishing sectional curvature
* hyperbolic geometry – constant negative sectional curvature.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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