Mathematical Sciences Publishers
We construct a conformal class of Lorentz metrics naturally associated with an abstract definite CR structure. If the CR structure is that of a pseudoconvex boundary in Cn we prove that the intrinsically constructed metric is the same as that discovered by Fefferman using a solution to a complex Monge-Ampère equation. The construction presented here relies on formal solutions of a linear equation, dζ = 0, and provides a relatively simple procedure for computing the metric.
FARRIS, Frank A. "An Intrinsic Construction of Fefferman's CR Metric."Pacific Journal of Mathematics 123 (1986): 33-45.