HYPERSURFACES IN P2 AND H2 WITH TWO DISTINCT PRINCIPAL CURVATURES

Abstract

AbstractIt is known that hypersurfaces in ${\mathbb C}$Pn or ${\mathbb C}$Hn for which the number g of distinct principal curvatures satisfies g ≤ 2, must belong to a standard list of Hopf hypersurfaces with constant principal curvatures, provided that n ≥ 3. In this paper, we construct a two-parameter family of non-Hopf hypersurfaces in ${\mathbb C}$P2 and ${\mathbb C}$H2 with g=2 and show that every non-Hopf hypersurface with g=2 is locally of this form.