On three dimensional real hypersurfaces in complex space forms (Q989195)

The authors prove that a real hypersurface \(M\) in the complex plane \(P_2(\mathbb C)\) or complex hyperbolic plane \(H_2(\mathbb C)\) is pseudo-parallel if and only if it is \(\eta\)-umbilical (\(\eta\) being the contact form induced on \(M\)). Then, they classify these hypersurfaces. Similarly, pseudo-symmetric Hopf hypersurfaces in \(P_2(\mathbb C)\) or \(H_2(\mathbb C)\) are classified. Particularly, Hopf hypersurfaces in \(P_2(\mathbb C)\) or \(H_2(\mathbb C)\) are pseudo-symmetric if and only if they are pseudo-Einstein.