This... is an outrageously over-simplified account of the assumptions and procedures... - Howard P. Robertson

In the sum <math>\sigma</math> of the three angles of a triangle (whose sides are arcs of s) is greater than two right angles [180°]; it can... be shown that this "spherical excess" is given by 2)<math>\sigma - \pi = K \delta</math>where <math>\delta</math> is the area of the spherical triangle and the angles are measured in s (in which 180° = <math>\pi</math> [radians]). Further, each full line (great circle) is of finite length <math>2 \pi R</math>, and any two full lines meet in two points—there are no parallels!

The field equation may... be given a geometrical foundation, at least to a first approximation, by replacing it with the requirement that the mean curvature of the space vanish at any point at which no heat is being applied to the medium—in complete analogy with... the general theory of relativity by which classical field equations are replaced by the requirement that the Ricci contracted curvature tensor vanish.

An "empty world," i.e., a homogeneous manifold at all points at which equations (1) are satisfied, has, according to the theory, a constant Riemann curvature, and any deviation from this fundamental solution is to be directly attributed to the influence of matter or energy.