, on the other hand, comprises a whole series of generally non-homogeneous spaces of which
(the homogeneous and homaloidal variety) is only one particular illustration. Hence,
by itself does not yield us any very definite information.
Likewise, a perfectly homogeneous spherical space of four dimensions, i.e., the type of space which corresponds to Riemann’s geometry of four dimensions, is given by
where
is a constant depending on the intensity of the curvature. On the other hand,