New characterization of Hopf hypersurfaces in nonflat complex space forms

Abstract

It is proved that the \(*\)-Ricci operator of a real hypersurface in a nonflat complex space form is Reeb parallel if and only if the hypersurface is Hopf. As an application of this result, we obtain a classification theorem of real hypersurfaces with parallel \(*\)-Ricci operators. These results answer some open questions posed by Kaimakamis and Panagiotidou a decade ago.