Sphere Embedding

A 4-sphere has positive curvature, with

(1)

(2)

Since

(3)

			(4)
			(5)

To stay on the surface of the sphere,

			(6)
			(7)
			(8)
			(9)
			(10)
			(11)

With the addition of the so-called expansion parameter, this is the Robertson-Walker line element.