On the Global Structure of Hopf Hypersurfaces in Complex Space Form

It is known that a tube over a Kahler submanifold in a complex form is a Hopf hypersurface. In some sense the reverse statement is true: a connected compact generic immersed C^(2n-1) regular Hopf hypersurface in the complex projective plane is a tube iver an irreducible algebraic variety. In the complex hyperbolic space a connected compact generic immersed C^(2n-1) regular Hopf hypersurface is a geodesic hypersphere