CR immersions and Lorentzian geometry

Abstract

Using tools from Lorentzian geometry (arising from the presence of the Fefferman metric) we prove a Takahashi type theorem (for a class of pseudohermitian immersionscoveredbyconnection-preservingequivariantimmersionsamongthetotal spacesofthecanonicalcirclebundles)thusrelatingthegeometryofapseudohermitian immersion from a strictly pseudoconvex CR manifold M into an odd dimensional sphere, to the spectrum of the sublaplacian on M.