Bull. Korean Math. Soc. 2010; 47(1): 1-15
Printed January 1, 2010
https://doi.org/10.4134/BKMS.2010.47.1.1
Copyright © The Korean Mathematical Society.
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
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
2007; 44(1): 157-172
2015; 52(5): 1621-1630
2013; 50(6): 2089-2101
2005; 42(2): 337-358
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd