Bulletin of the
Korean Mathematical Society BKMS

In this paper, we prove that if the structure Jacobi operator $R_{\xi}$ is $\xi$-parallel and $R_{\xi}$ commutes with the Ricci tensor $S$, then a real hypersurface with non-negative scalar curvature of a nonflat complex space form ${\rm M}_n(c)$ is a Hopf hypersurface. Further, we characterize such Hopf hypersurface in ${\rm M}_n(c)$.

Keywords: real hypersurface, structure Jacobi operator, Ricci tensor, Hopf hypersurface

MSC numbers: 53C40, 53C15