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

 

Rigidity of pseudoconformal connections


Authors: Michael Markowitz and Roger Schlafly
Journal: Trans. Amer. Math. Soc. 276 (1983), 133-135
MSC: Primary 32F25; Secondary 53B15
MathSciNet review: 684497
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Abstract: Let $ {M^{2n - 1}}(n \geqslant 3)$ be a strictly pseudoconvex abstract $ {\text{CR}}$-hypersurface $ {\text{CR}}$-immersed in the unit sphere in $ {{\mathbf{C}}^N}$. We show that the pseudoconformal connection induced on $ M$ by the standard flat connection agrees with the intrinsic normal connection of Cartan-Chern-Tanaka if and only if $ M$ is pseudoconformally flat. In this case $ M$ is a piece of the transverse intersection of $ {S^{2N - 1}}$ with a complex $ n$-plane in $ {{\mathbf{C}}^N}$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0684497-2
PII: S 0002-9947(1983)0684497-2
Article copyright: © Copyright 1983 American Mathematical Society