The Fefferman metric and pseudo-Hermitian invariants

Abstract

C. Fefferman has shown that a real strictly pseudoconvex hypersurface in complex n n -space carries a natural conformal Lorentz metric on a circle bundle over the manifold. This paper presents two intrinsic constructions of the metric, valid on an abstract CR {\text {CR}} manifold. One is in terms of tautologous differential forms on a natural circle bundle; the other is in terms of Webster’s pseudohermitian invariants. These results are applied to compute the connection and curvature forms of the Fefferman metric explicitly.