A characterization of homogeneous real hypersurfaces of types (C), (D) and (E) in a complex projective space

We give a necessary and sufficient condition that a Riemannian manifold M2n−1 isometrically immersed into a complex projective space CPn(c) is locally congruent to one of homogeneous real hypersurfaces of types (C), (D) and (E) in this ambient space in terms of its restricted principal curvature distributions.