HYPERSURFACES IN P 2 AND H 2 WITH TWO DISTINCT PRINCIPAL CURVATURES

Source abstract

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