A classification of pseudo-Einstein hypersurfaces in \(\mathbb CP^{2}\) (Q2474219)

In the paper under review, the authors present a classification of pseudo-Einstein hypersurfaces \(M^3\) in the complex space form \(\mathbb{C} P^2\) of constant holomorphic curvature \(4c= {4\over r^2}\). Specifically: (i) Such a hypersurface must be Hopf. (ii) In addition to the geodesic spheres, all tubes of radius \(\frac\pi4 r\) around holomorphic curves are pseudo-Einstein. (iii) All pseudo-Einstein hypersurfaces in \(\mathbb{C} P^2\) are generically of this form. (iv) The only compact pseudo-Einstein hypersurfaces are the geodesic spheres.