# REAL HYPERSURFACES IN COMPLEX SPACE FORMS WITH ε-PARALLEL RICCI TENSOR AND STRUCTURE JACOBI OPERATOR

• Ki, U-Hang (The National Academy of Sciences) ;
• Perez Juan De Dios (Department de Geometria y Topologia Facultad de Ciencias Universidad de Granada) ;
• Santos Florentino G. (Departamento de Geometria y Topologia Facultad de Ciencias Universided de Granada) ;
• Suh Young-Jin (Department of Mathematics Kyungpook university)
• Published : 2007.03.31
• 118 7

#### Abstract

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 ${\nabla}_{\varepsilon}S=0\;and\;{\nabla}_{\varepsilon}R_{\varepsilon}=0,\;where\;S\;and\;R_{\varepsilon}$ 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

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