Hopf hypersurfaces of small Hopf principal curvature in $${\mathbb{C}{\rm H}^2}$$

Abstract

Using the methods of moving frames and exterior differential systems, we show that there exist Hopf hypersurfaces in complex hyperbolic space \({\mathbb{C}{\rm H}^2}\) with any specified value of the Hopf principal curvature α less than or equal to the corresponding value for the horosphere. We give a construction for all such hypersurfaces in terms of Weierstrass-type data, and also obtain a classification of pseudo-Einstein hypersurfaces in \({\mathbb{C}{\rm H}^2}\).