J. Korean Math. Soc. 2007; 44(2): 307-326
Printed March 1, 2007
Copyright © The Korean Mathematical Society.
U-Hang Ki, Juan De Dios Perez, Florentino G. Santos, and Young Jin Suh
The National Academy of Sciences, Universidad de Granada, Universidad de Granada, Kyungpook University
We know that there are no real hypersurfaces with parallel Ricci tensor or parallel structure Jacobi operator in a nonflat complex space form (See [4], [6], [10] and [11]). In this paper we investigate real hypersurfaces $M$ in a nonflat complex space form $M_n (c)$ under the condition that $\nabla _{\xi}S=0$ and $\nabla _{\xi}{R_{\xi}}=0$, where $S$ and $R_{\xi}$ respectively denote the Ricci tensor and the structure Jacobi operator of $M$ in $M_n (c)$.
Keywords: real hypersurface, structure Jacobi operator, Ricci tensor, Hopf hypersurface
MSC numbers: Primary 53C40; Secondary 53C15
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