Hypersurfaces in $C{P}^2$ and $C{H}^2$ with two distinct principal curvatures

Abstract

It is known that hypersurfaces in $C{P}^n$ or $C{H}^n$ 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 $C{P}^2$ and $C{H}^2$ with $g=2$ and show that every non-Hopf hypersurface with $g=2$ is locally of this form.

15 pages; revised version to appear in Glasgow Mathematical Journal

References in corpus (1)

• Real hypersurfaces with two principal curvatures in complex projective and hyperbolic planes