A unique equivalence is established between the Riemann curvature tensor and two spinors. The fourteen invariants which can be constructed from the curvature tensor are listed in terms of the spinors. The vanishing of the invariants for several different types of spaces is described. A classification of Einstein spaces is made together with a few additional remarks concerning classification of spaces.

• Received 11 June 1958

DOI:https://doi.org/10.1103/PhysRev.113.357