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

Thomas A. Ivey; Patrick J. Ryan

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

Differential Geometry 2015-01-28 v2

Authors: Thomas A. Ivey , Patrick J. Ryan

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.

Keywords

hypersurfaces principal curvatures hopf hypersurfaces complex projective space complex hyperbolic space differential geometry

Cite

@article{arxiv.1311.1973,
  title  = {Hypersurfaces in $CP^2$ and $CH^2$ with two distinct principal curvatures},
  author = {Thomas A. Ivey and Patrick J. Ryan},
  journal= {arXiv preprint arXiv:1311.1973},
  year   = {2015}
}

Comments

15 pages; revised version to appear in Glasgow Mathematical Journal

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