  In this paper we derive 4-dimensional General Relativity from three
dimensions, using the intrinsic spatial geometry inherent in Yang--Mills theory
which has been exposed by previous authors as well as as some properties of the
Ashtekar variables. We provide various interesting relations, including the
fact that General Relativity can be written as a Yang--Mills theory where the
antiself-dual Weyl curvature replaces the Yang--Mills coupling constant. We
have generalized the results of some previous authors, covering Einsteins
spaces, to include more general spacetime geometries.
