Classification of the Ricci tensor

This paper contains a classification of the Ricci tensorR. The method of derivation is analogous to the spinor version of the Petrov classification of the Weyl tensor. It is shown how the various classes are related to the number and type of eigenvectors and eigenvalues ofR. The classification is useful in the geometrization of various fields. The case of a real scalar field is treated in detail.Supported in part by the National Research Council of Canada.