On real hypersurfaces of a complex projective space. II (Q1192585)

[Part I, see Math. Z. 202, No. 3, 299-311 (1989; Zbl 0661.53015).] It is well-known that there exist no real hypersurfaces \(M\) with parallel second fundamental form \(A\) in a complex projective space. The main purpose of this paper is to classify real hypersurfaces \(M\) satisfying \(\nabla_ \xi A=0\) (that is, \(A\) is parallel in the direction of the characteristic vector field \(\xi\) of \(M\)) in \(P_ n(\mathbb{C})\). The authors emphasize that there exist many non-homogeneous real hypersurfaces satisfying \(\nabla_ \xi A=0\) in \(P_ n(\mathbb{C})\).