Gauss-Codazzi tensor fields and the Bonnet immersion theorem.
We study homogeneous real hypersurfaces having no focal submanifolds in a complex hyperbolic space. They are called Lie hypersurfaces in this space. We clarify the geometry of Lie hypersurfaces in terms of their sectional curvatures, the behavior of the characteristic vector field and their holomorphic distributions.
We characterize homogeneous real hypersurfaces ’s of type , and of a complex projective space in the class of real hypersurfaces by studying the holomorphic distribution of .