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