Open AccessPseudoconformal Geometry of Hypersurfaces in C n +1
Author(s) -
D. Burns,
Steven Shnider
Publication year - 1975
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.72.6.2433
Subject(s) - hypersurface , connection (principal bundle) , mathematics , vector bundle , pure mathematics , conformal map , bundle , geometry , conformal geometry , mathematical analysis , conformal symmetry , materials science , composite material
The pseudoconformal geometry (CR structure) of a real hypersurfaceM in Cn +1is 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 bundleY overM . 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 overM . 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 +1is given.