Hopf Hypersurfaces of Small Hopf Principal Curvature in CH^2

TL;DR

This paper classifies and constructs Hopf hypersurfaces in complex hyperbolic space CH^2 with small Hopf principal curvature, using moving frames and exterior differential systems, and explores pseudo-Einstein hypersurfaces.

Contribution

It provides a classification and explicit construction of Hopf hypersurfaces with specified small Hopf principal curvature in CH^2.

Findings

Existence of Hopf hypersurfaces with any specified small Hopf principal curvature.

Construction of these hypersurfaces using Weierstrass-type data.

Classification of pseudo-Einstein hypersurfaces in CH^2.

Abstract

Using the methods of moving frames and exterior differential systems, we show that there exist Hopf hypersurfaces in complex hyperbolic space CH^2 with any specified value of the Hopf principal curvature 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 CH^2.