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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 standardlist of Hopf hypersurfaces with constant principal curvatures, provided that $n\ge 3$. In this paper, we construct a 2-parameter family of non-Hopfhypersurfaces in $CP^2$ and $CH^2$ with $g=2$ and show that every non-Hopfhypersurface with $g=2$ is locally of this form.

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