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

• Journal title : Honam Mathematical Journal
• Volume 32, Issue 4,  2010, pp.747-761
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2010.32.4.747
Title & Authors
ON THE STRUCTURE JACOBI OPERATOR AND RICCI TENSOR OF REAL HYPERSURFACES IN NONFLAT COMPLEX SPACE FORMS
Kim, Soo-Jin;

Abstract
It is known that there are no real hypersurfaces with parallel structure Jacobi operator $\small{R_{\xi}}$ (cf.[16], [17]). In this paper we investigate real hypersurfaces in a nonflat complex space form using some conditions of the structure Jacobi operator $\small{R_{\xi}}$ which are weaker than $\small{{\nabla}R_{\xi}}$ = 0. Under further condition $\small{S\phi={\phi}S}$ for the Ricci tensor S we characterize Hopf hypersurfaces in a complex space form.
Keywords
Hopf hypersurface;structure Jacobi operator;Ricci tensor;
Language
English
Cited by
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