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 Characterizations of real hypersurfaces of type A in a complex space form Bull. Korean Math. Soc. 2010 Vol. 47, No. 1, 1-15 https://doi.org/10.4134/BKMS.2010.47.1.1Printed January 1, 2010 U-Hang Ki, In-Bae Kim, and Dong Ho Lim The National Academy of Science, Hankuk University of Foreign Studies, and Hankuk University of Foreign Studies Abstract : Let $M$ be a real hypersurface with almost contact metric structure $(\phi, g, \xi, \eta)$ in a complex space form $M_n(c)$, $c \neq 0$. In this paper we prove that if $R_\xi \mathcal L_\xi g=0$ holds on $M$, then $M$ is a Hopf hypersurface in $M_n(c)$, where $R_\xi$ and $\mathcal L_x$ denote the structure Jacobi operator and the operator of the Lie derivative with respect to the structure vector field $\xi$ respectively. We characterize such Hopf hypersurfaces of $M_n(c)$. Keywords : real hypersurface, structure Jacobi operator, Hopf hypersurface MSC numbers : Primary 53C40; Secondary 53C15 Downloads: Full-text PDF