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arXiv · 1311.1973

Hypersurfaces in $CP^2$ and $CH^2$ with two distinct principal curvatures

Thomas A. Ivey·Patrick J. Ryan
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Abstract

It is known that hypersurfaces in $CP^n$ or $CH^n$ for which the number $g$ of distinct principal curvatures satisfied $g \le 2$ must belong to a standard list of Hopf hypersurfaces with constant principal curvatures, provided that $n \ge 3$. In this paper, we construct a 2-parameter family of non-Hopf hypersurfaces in $CP^2$ and $CH^2$ with $g=2$ and show that every non-Hopf hypersurface with $g=2$ is locally of this form.

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Thomas A. Ivey, Patrick J. Ryan. 2015-01-27. Hypersurfaces in $CP^2$ and $CH^2$ with two distinct principal curvatures. https://arxiv.org/abs/1311.1973

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