For a circle which has constant curvature, every point is a vertex.

By definition, these are the surfaces X with constant curvature 0.

He showed that spaces of constant curvature could differ in topological structure.

In particular, most Zoll surfaces do not have constant curvature.

In most cases including the cases of constant curvature, the geometry is unique.

Well, balls and oranges, for example, have constant positive curvature.

Define as the 2-dimensional metric space of constant curvature .

Next, the overall shape must have constant positive curvature.

In mathematics, constant curvature is a concept from differential geometry.

For example, a sphere is a surface of constant positive curvature.