CR-hypersurfaces in a space with a pseudoconformal connection

Markowitz, Michael J.

doi:10.1090/S0002-9947-1983-0684496-0

CR-hypersurfaces in a space with a pseudoconformal connection
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by Michael J. Markowitz PDF

Trans. Amer. Math. Soc. 276 (1983), 117-132 Request permission

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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