  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
