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http://dx.doi.org/10.5831/HMJ.2010.32.4.747

ON THE STRUCTURE JACOBI OPERATOR AND RICCI TENSOR OF REAL HYPERSURFACES IN NONFLAT COMPLEX SPACE FORMS  

Kim, Soo-Jin (Department of Mathematics, Chosun University)
Publication Information
Honam Mathematical Journal / v.32, no.4, 2010 , pp. 747-761 More about this Journal
Abstract
It is known that there are no real hypersurfaces with parallel structure Jacobi operator $R_{\xi}$ (cf.[16], [17]). In this paper we investigate real hypersurfaces in a nonflat complex space form using some conditions of the structure Jacobi operator $R_{\xi}$ which are weaker than ${\nabla}R_{\xi}$ = 0. Under further condition $S\phi={\phi}S$ for the Ricci tensor S we characterize Hopf hypersurfaces in a complex space form.
Keywords
Hopf hypersurface; structure Jacobi operator; Ricci tensor;
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Times Cited By KSCI : 2  (Citation Analysis)
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