Hopf Hypersurfaces of Small Hopf Principal Curvature in CH²

2008/12/24 by Ivey, Thomas A., Ryan, Patrick J.
#53C25 #53C40 #53C55 #58A15 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0812.4535

Abstract

Using the methods of moving frames and exterior differential systems, we show that there exist Hopf hypersurfaces in complex hyperbolic space CH² 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 CH².

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