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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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참고문헌 (19)
참고문헌 신청
J. Berndt / 1989 / Real hypersurfaces with constant principal curvatures in complex hyperbolic spaces / J. Reine Angew. Math. 395:132~141
J. Berndt / 2007 / Cohomogeneity one actions on noncompact sym-metric spaces of rank one / Trans. Amer. Math. Soc. 359:3425~3438
J. T. Cho / 1998 / Jacobi operators on real hypersurfaces of a complex projective space / Tsukuba J. Math. 22:145~156
J. T. Cho / 1998 / Real hypersurfaces of a complex projective space in terms of Jacobi operators / Acta Math. Hungar. 80:155~167
J. T. Cho / 2008 / Real hypersurfaces in a complex space form with Reeb °ow symmetric Jacobi operator / Canadian Math. Bull. 51:359~371
J. Berndt / 2007 / Cohomogeneity one actions on noncompact sym-metric spaces of rank one / Trans. Amer. Math. Soc. 359:3425~3438
J. T. Cho / 1998 / Jacobi operators on real hypersurfaces of a complex projective space / Tsukuba J. Math. 22:145~156
J. T. Cho / 1998 / Real hypersurfaces of a complex projective space in terms of Jacobi operators / Acta Math. Hungar. 80:155~167
J. T. Cho / 2008 / Real hypersurfaces in a complex space form with Reeb °ow symmetric Jacobi operator / Canadian Math. Bull. 51:359~371
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