On the global structure of Hopf hypersurfaces in a complex space form
AA Borisenko - Illinois Journal of Mathematics, 2001 - projecteuclid.org
Illinois Journal of Mathematics, 2001•projecteuclid.org
It is known that a tube over a Kähler submanifold in a complex space 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 space is a tube
over an irreducible algebraic variety. In the complex hyperbolic space a connected compact
generic immersed $ C^{2n-1} $ regular Hopf hypersurface is a geodesic hypersphere.
hypersurface. In some sense the reverse statement is true: a connected compact generic
immersed $ C^{2n-1} $ regular Hopf hypersurface in the complex projective space is a tube
over an irreducible algebraic variety. In the complex hyperbolic space a connected compact
generic immersed $ C^{2n-1} $ regular Hopf hypersurface is a geodesic hypersphere.
It is known that a tube over a Kähler submanifold in a complex space form is a Hopf hypersurface. In some sense the reverse statement is true: a connected compact generic immersed regular Hopf hypersurface in the complex projective space is a tube over an irreducible algebraic variety. In the complex hyperbolic space a connected compact generic immersed regular Hopf hypersurface is a geodesic hypersphere.
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