Pseudoconformal Geometry of Hypersurfaces in Cn+1

摘要

The pseudoconformal geometry (CR structure) of a real hypersurface M in Cⁿ⁺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 Cⁿ⁺¹ is given.