Claim: Hypersphere, a set of points at a constant distance from the center that is introduced by Duncan Sommerville, is a manifold of codimension one in which its radius and curvature have a direct relationship.
Evidence: In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its centre. It is a manifold of codimension one—that is, with one dimension less than that of the ambient space. As the hypersphere's radius increases, its curvature decreases. The term hypersphere was introduced by Duncan Sommerville in his 1914 discussion of models for non-Euclidean geometry.