The significance of curvature in general relativity

In General Relativity, there are several traditional ways of interpreting the curvature of space-time, expressed either through the curvature tensor or the sectional curvature function. This essay asks what happens if curvature is treated on a more primitive level, that is, if the curvature is prescribed, what information does one have about the metric and associated connection of space-time. It turns out that a surprising amount of information is available, not only about the metric and connection, but also, through Einstein's equations, about the algebraic structure of the energy-momentum tensor. (author)