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 immersions covered by connection-preserving equivariant immersions among the total spaces of the canonical circle bundles) thus relating the geometry of a pseudohermitian immersion from a strictly pseudoconvex CR manifold $$M$$ into an odd dimensional sphere, to the spectrum of the sublaplacian on $$M$$ .