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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Twistor CR manifolds and three-dimensional conformal geometry


Author: Claude R. LeBrun
Journal: Trans. Amer. Math. Soc. 284 (1984), 601-616
MSC: Primary 32F25; Secondary 32L25, 53A30, 53C15
MathSciNet review: 743735
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Abstract: A CR (i.e. partially complex) $ 5$-manifold is contructed as a sphere bundle over an arbitrary $ 3$-manifold with conformal metric. This so-called twistor $ CR$ manifold is show to capture completely the original geometry, and necessary and sufficient conditions are given for an abstract CR manifold to arise via the construction. The above correspondence is then used to prove that a twistor CR manifold is locally imbeddable as a real hypersurface in $ {{\mathbf{C}}^3}$ only if it is real-analytic with respect to a suitable atlas.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0743735-9
PII: S 0002-9947(1984)0743735-9
Article copyright: © Copyright 1984 American Mathematical Society