ON CHARACTERIZATIONS OF REAL HYPERSURFACES IN A COMPLEX SPACE FORM IN TERMS OF THE JACOBI OPERATORS

ON CHARACTERIZATIONS OF REAL HYPERSURFACES IN A COMPLEX SPACE FORM IN TERMS OF THE JACOBI OPERATORS

The shape operator or second fundamental tensor of a real hypersurface in $M_n(c)$ will be denoted by A, and the induced almost contact metric structure of the real hypersurface by (${\phi}$, <, >,${\xi}$, ${\eta}$). The purpose of this paper is to prove that is no ruled real hypersurface M in a complex space form $M_n(c)$, $c{\neq}0$, $n{\geq}3$, who satisfies $R_{\xi}{\phi}={\phi}R_{\xi}$ on M.

(0)

(0)

(0)

(0)