CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM USED BY THE ζ-PARALLEL STRUCTURE JACOBI OPERATOR

• Journal title : Honam Mathematical Journal
• Volume 30, Issue 3,  2008, pp.535-550
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2008.30.3.535
Title & Authors
CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM USED BY THE ζ-PARALLEL STRUCTURE JACOBI OPERATOR
Kim, Nam-Gil; Ki, U-Hang; Kurihara, Hiroyuki;

Abstract
Let M be a real hypersurface of a complex space form with almost contact metric structure $\small{({\phi},{\xi},{\eta},g)}$. In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator $R_{\xi} Keywords complex;space form;real hypersurface;structure Jacobi operator; Language English Cited by 1. CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A NONFLAT COMPLEX SPACE FORM WHOSE STRUCTURE JACOBI OPERATOR IS ξ-PARALLEL, Honam Mathematical Journal, 2009, 31, 2, 185 References 1. J. Berndt, Real hypersurfaces with constant principal curvatures in complex hyperblic spaces, J. Reine Angew. Math. 395 (1989) 132-141. 2. T. E. Cecil and P. J. Ryan, Focal sets and real hypersurfaces in complex projective space, Trans. Amer. Math. Soc. 269 (1982) 481-499. 3. J. T. Cho and U-H. Ki, Real hypersurfaces of a complex projective space in terms of Jacobi operators, Acta Math. Hungar. 80 (1998) 155-167. 4. J. T. Cho and U-H. Ki, Jacobi operators on real hypersurfaces of a complex projective space, Tsukuba. J. Math. 22 (1998) 145-156. 5. J. T. Cho and U-H. Ki, Real hypersurfaces in complex space form with Reeb flow symmetric structure Jacobi operetor, to appear in Canadian Math. Bull. 6. U-H. Ki, Real hypersurfaces with pararell Ricci tensor of a complex space form, Tsukuba J. Math. 13 (1989) 73-81. 7. U-H. Ki and H. Liu, Some characterizations of real hypersurfaces of type (A) in a nonflat complex space form, Bull. Korean. Math. Soc. 44 (2007) 152-157. 8. U-H. Ki and Y. J. Suh, On real hypersurfaces of a complex space form, Math J. Okayama Univ. 32 (1990) 207-221. 9. U. K. Kim, Nonexistence of Ricci-parallel real hypersurfaces in$P_2{\mathbb{C}}$or$H_2{\mathbb{C}}\$, Bull. Korean. Math. Soc. 41 (2004) 699-708.

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