Bulletin of the
Korean Mathematical Society BKMS

In this paper, we proved that a real hypersurface of a complex hyperbolic space satisfying $L_\xi S = 0$ and $S\xi = \sigma\xi$ for the Ricci tensor $S$, then the structure vector field $\xi$ is principal, where $L_\xi$ denotes the Lie derivative with respect to $\xi$.

Keywords: Real hypersurfaces, Ricci tensor, Lie derivative, principal curvature vector.

MSC numbers: 53C15, 53C45