An intrinsic construction of Fefferman’s CR metric

Frank Albert Farris

Vol. 123 (1986), No. 1, 33–45

DOI: 10.2140/pjm.1986.123.33

Abstract

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.

Mathematical Subject Classification 2000

Primary: 53C50

Secondary: 32C05, 32F25

Milestones

Received: 5 November 1984

Published: 1 May 1986