Honam Mathematical Journal (호남수학학술지)

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

  • Kim, Soo-Jin (Department of Mathematics, Chosun University)
  • Received : 2010.11.19
  • Accepted : 2010.12.06
  • Published : 2010.12.25
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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.

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References

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