Characterizations of real hypersurfaces of type A in a complex space form
Bull. Korean Math. Soc. 2010 Vol. 47, No. 1, 1-15
Printed 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
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