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

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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 \({\mathbb{C}{\rm H}^2}\).

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Authors and Affiliations

  1. Department of Mathematics, College of Charleston, 66 George St., Charleston, SC, 29424, USA

    Thomas A. Ivey

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S4K1, Canada

    Patrick J. Ryan

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  1. Thomas A. Ivey
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  2. Patrick J. Ryan
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Correspondence to Patrick J. Ryan.

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Ivey, T.A., Ryan, P.J. Hopf hypersurfaces of small Hopf principal curvature in \({\mathbb{C}{\rm H}^2}\) . Geom Dedicata 141, 147–161 (2009). https://doi.org/10.1007/s10711-008-9349-7

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  • DOI: https://doi.org/10.1007/s10711-008-9349-7

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