Journal of the
Korean Mathematical Society JKMS

We know that there are no real hypersurfaces with parallel Ricci tensor or parallel structure Jacobi operator in a nonflat complex space form (See [4], [6], [10] and [11]). In this paper we investigate real hypersurfaces $M$ in a nonflat complex space form $M_n (c)$ under the condition that $\nabla _{\xi}S=0$ and $\nabla _{\xi}{R_{\xi}}=0$, where $S$ and $R_{\xi}$ respectively denote the Ricci tensor and the structure Jacobi operator of $M$ in $M_n (c)$.

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

MSC numbers: Primary 53C40; Secondary 53C15