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
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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