We may also mention that in addition to the Riemann-Christoffel tensor
, Einstein has made use of the other tensor
(previously discovered by Ricci), which in four-dimensional space is defined by ten separate relations between the values of the
’s at a point and their values at neighbouring points. The vanishing of this other tensor
at every point, that is to say, the vanishing of the ten new component expressions at every point, is insufficient in itself to ensure the Euclideanism of the space; although, of course, this vanishing imposes certain restrictions on the space’s non-Euclideanism. These restrictions are less severe than those defined by the vanishing of the twenty components of the Riemann-Christoffel tensor, which ensures perfect flatness; on the other hand, they are more stringent than those imposed by a mere vanishing of the Gaussian curvature
