### CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM

Ki, U-Hang;Kim, In-Bae;Lim, Dong-Ho

• 발행 : 2010.01.31
• 36 5

#### 초록

Let M be a real hypersurface with almost contact metric structure $(\phi,g,\xi,\eta)$ in a complex space form $M_n(c)$, $c\neq0$. In this paper we prove that if $R_{\xi}L_{\xi}g=0$ holds on M, then M is a Hopf hypersurface in $M_n(c)$, where $R_{\xi}$ and $L_{\xi}$ 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 $M_n(c)$.

#### 키워드

real hypersurface;structure Jacobi operator;Hopf hypersurface

#### 참고문헌

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#### 피인용 문헌

1. On characterizations of real hypersurface in complex space form with Codazzi type structure Lie operator vol.173, pp.3, 2014, https://doi.org/10.4134/BKMS.2010.47.1.001
2. On Characterizations of Hopf Hypersurfaces in a Nonflat Complex Space Form with Anti-commuting Operators vol.71, pp.1-2, 2017, https://doi.org/10.4134/BKMS.2010.47.1.001
3. Real hypersurfaces with Killing type operators in a nonflat complex space form 2017, https://doi.org/10.4134/BKMS.2010.47.1.001