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1983•Transactions of the American Mathematical SocietyOpen access

CR-hypersurfaces in a space with a pseudoconformal connection

Michael J. Markowitz

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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 M is so situated that it inherits the structure of a CR {\text {CR}} -hypersurface from the ambient space. M 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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In this paper we study a submanifold in a space with a pseudoconformal connection. We assume that the submanifold M M is so situated that it inherits the structure of a CR {\text {CR}} -hypersurface from the ambient space. M 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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Available abstract

In this paper we study a submanifold in a space with a pseudoconformal connection. We assume that the submanifold M M is so situated that it inherits the structure of a CR {\text {CR}} -hypersurface from the ambient space. M 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.

Key concepts: Submanifold, Algorithm, Connection (principal bundle), Annotation, Hypersurface, Type (biology), Mathematics, Computer science

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