A classification of pseudo-Einstein hypersurfaces in CP2CP2

In this paper we present a classification of the pseudo-Einstein hypersurfaces M3M3 in the complex space form CP2CP2 of constant holomorphic curvature 4c=4r2. Specifically, (i) Such a hypersurface must be Hopf; (ii) In addition to the geodesic spheres, all tubes of radius π4r around holomorphic curves are pseudo-Einstein; (iii) All pseudo-Einstein hypersurfaces in CP2CP2 are generically (in a sense we will make precise) of this form; (iv) The only compact pseudo-Einstein hypersurfaces are the geodesic spheres.