Bulletin of the
Korean Mathematical Society BKMS

Niebergall and Ryan posed many open problems on real hypersurfaces in complex space forms. One of them is ``Are there any Ricci-parallel real hypersurfaces in complex projective space $P_2\mathbb{C}$ or complex hyperbolic space $H_2\mathbb{C}$?" The purpose of present paper is to prove the nonexistence of such hypersurfaces.

Keywords: Ricci-parallel hypersurface, real hypersurface, complex space form

MSC numbers: Primary 53C40; Secondary 53C15