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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The Fefferman metric and pseudo-Hermitian invariants

Author: John M. Lee
Journal: Trans. Amer. Math. Soc. 296 (1986), 411-429
MSC: Primary 32F25; Secondary 53B25
MathSciNet review: 837820
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Abstract: C. Fefferman has shown that a real strictly pseudoconvex hypersurface in complex $n$-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 ${\text {CR}}$ 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.

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Article copyright: © Copyright 1986 American Mathematical Society