Curvature structure in general relativity

This paper investigates the extent to which the curvature structure of space-time determines the metric stucture. It continues the work of earlier papers by prescribing the curvature structure and the curvature covariant derivatives up to certain orders. It is shown that, with the exception of the so-called generalized pp waves, the curvature and its first and second covariant derivatives essentially determine the metric up to coordinate transformations.