JACOBI OPERATORS ALONG THE STRUCTURE FLOW ON REAL HYPERSURFACES IN A NONFLAT COMPLEX SPACE FORM II

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Let M be a real hypersurface of a complex space form with almost contact metric structure (<TEX>${\phi}$</TEX>, <TEX>${\xi}$</TEX>, <TEX>${\eta}$</TEX>, g). In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator <TEX>$R_{\xi}=R({\cdot},\;{\xi}){\xi}$</TEX> is <TEX>${\xi}$</TEX>-parallel. In particular, we prove that the condition <TEX>${\nabla}_{\xi}R_{\xi}=0$</TEX> characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic space when <TEX>$R_{\xi}{\phi}S=R_{\xi}S{\phi}$</TEX> holds on M, where S denotes the Ricci tensor of type (1,1) on M.