Pseudoconformal geometry of hypersurfaces in C.
The pseudoconformal geometry (CR structure) of a real hypersurface M in C(n+1) is reviewed. We give an alternative formulation of a theorem of Cartan-Tanaka-Chern on the existence of a unique normalized Cartan connection on a principal bundle Y over M. A family of curves defined by this connection, called chains, is shown to be the projection of light rays of a conformal equivalence class of Lorentz metrics on a trivial circle bundle over M. The simply connected homogeneous manifolds locally CR equivalent to the sphere are classified. A theorem on moduli for deformations of the complex structure on the ball in C(n+1) is given.
Department of Mathematics, Princeton University, Princeton, New Jersey 08540.
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Burns
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Shnider