Bulletin of the
Korean Mathematical Society BKMS

We study a real hypersurface $M$ satisfying $L_\xi S = 0$ and $R_\xi S = SR_\xi$ in a complex hyperbolic space $H_n{\Bbb C}$, where $S$ is the Ricci tensor of type (1,1) on $M$, $L_\xi$ and $R_\xi$ denotes the operator of the Lie derivative and the Jacobi operator with respect to the structure vector field $\xi$ respectively.

Keywords: real hypersurface, principal curvature vector, Lie derivative, Jacobi operator

MSC numbers: Primary 53C40; Secondary 53C15