On real hypersurfaces of a complex hyperbolic space
Bull. Korean Math. Soc. 1997 Vol. 34, No. 2, 173-184
Eun-Hee Kang and U-Hang Ki Kyungpook University
Abstract : 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.