Hopf Hypersurfaces with Constant Principal Curvatures in Complex Projective or Complex Hyperbolic Spaces

Abstract

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.