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Transactions of the American Mathematical Society

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

 

 

CR-hypersurfaces in a space with a pseudoconformal connection


Author: Michael J. Markowitz
Journal: Trans. Amer. Math. Soc. 276 (1983), 117-132
MSC: Primary 32F25; Secondary 53B25
DOI: https://doi.org/10.1090/S0002-9947-1983-0684496-0
MathSciNet review: 684496
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Abstract: In this paper we study a submanifold in a space with a pseudoconformal connection. We assume that the submanifold $ M$ is so situated that it inherits the structure of a $ {\text{CR}}$-hypersurface from the ambient space. $ M$ then supports two natural Cartan connections, the normal pseudoconformal connection of Cartan-Chern-Tanaka and an induced pseudoconformal connection. Analogues of the Gauss-Codazzi equations are derived and applied to determine necessary and sufficient conditions for the equivalence of these connections.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0684496-0
Article copyright: © Copyright 1983 American Mathematical Society