CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A NONFLAT COMPLEX SPACE FORM WHOSE STRUCTURE JACOBI OPERATOR IS ξ-PARALLEL

• Journal title : Honam Mathematical Journal
• Volume 31, Issue 2,  2009, pp.185-201
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2009.31.2.185
Title & Authors
CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A NONFLAT COMPLEX SPACE FORM WHOSE STRUCTURE JACOBI OPERATOR IS ξ-PARALLEL
Kim, Nam-Gil;

Abstract
Let M be a real hypersurface with almost contact metric structure $\small{({\phi},{\xi},{\eta},g)}$ of a nonflat complex space form whose structure Jacobi operator $R_{\xi} Keywords real hypersurface;structure Jacobi operator;Ricci tensor;Hopf hypersurface; Language English Cited by References 1. J. Berndt, Real hypersurfaces with constant principal curvatures in complex hyperbolic spaces, J. Reine Angew. Math. 395 (1989), 132-141. 2. J. Berndt And H. Tamaru, Cohomogeneity one actions on noncompact symmetric spaces of rank one, Trans. Amer. Math. Soc. 359 (2007), 3425-3438. 3. T. E. Cecil And P. J. Ryan, Focal sets and real hypersurfaces in complex projective space, Trans. Amer. Math. Soc. 269 (1982), 481-499. 4. J. T. Cho and U-H. Ki, Real hypersurfaces of a complex projective space in terms of Jacobi operators, Acta Math. Hungar. 80 (1998), 155-167. 5. J. T. Cho and U-H. Ki, Real hypersurfaces in a complex space form with symmetric Jacobi Reeb flow, Canadian Math. Bull. 51 (2008), 359-371. 6. U-H. Ki, H. Kurihara and R. Takagi, Jacobi operators along the structure flow on real hypersurfaces in a nonflat complex space form, to appear in Tsukuba J. Mach. 7. U-H. Ki and H. Liu, Some characterizations of real hypersurces of type (A) in a nonflat complex space form, Bull. Korean Math. Soc. 44 (2007), 152-172. 8. U-H. Ki, J. D. Perez, F. G. Santos end Y. J. Suh, Real hypersurfaces in complex space forms with$\xi$-parallel Ricci tensor and structure Jacobi operator, J. Korean Math. Soc. 44 (2007), 307-326. 9. U-H. Ki and Y. J. Suh, On real hypersurfaces of a complex space form, Math. J. Okayama Univ. 32 (1990), 207-221. 10. N.-G. Kim, U-H. Ki and H. Kurihara, Characterizations of real hypersurfaces of type A in complex space form used by the$\xi\$-parallel structure Jacobi operator, Honam Math. J. 30 (2008), 535-550.

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