A real hypersurface of a complex space form is called a Hopf hypersurface if the characteristic vector field $\xi=-JN$ on $M$ is a principal curvature vector. The main purpose of this paper is to obtain several simple geometric characterizations of all Hopf hypersurfaces with constant principal curvatures in nonflat complex space forms.
"Hopf Hypersurfaces with Constant Principal Curvatures in Complex Projective or Complex Hyperbolic Spaces." Tokyo J. Math. 24 (1) 133 - 152, June 2001. https://doi.org/10.3836/tjm/1255958318