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 Real hypersurfaces of the Jacobi operator with respect to the structure vector field in a complex space form Bull. Korean Math. Soc. 2005 Vol. 42, No. 2, 279-294 Published online June 1, 2005 Seong Soo Ahn Dongshin University Abstract : 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 Full-Text :