Browse > Article
http://dx.doi.org/10.5666/KMJ.2021.61.1.181

Certain Characterization of Real Hypersurfaces of type A in a Nonflat Complex Space Form  

Ki, U-Hang (The National Academy of Siences)
Publication Information
Kyungpook Mathematical Journal / v.61, no.1, 2021 , pp. 181-190 More about this Journal
Abstract
Let M be a real hypersurface with almost contact metric structure (ϕ, ��, η, g) in a nonflat complex space form Mn(c). We denote S and R�� by the Ricci tensor of M and by the structure Jacobi operator with respect to the vector field �� respectively. In this paper, we prove that M is a Hopf hypersurface of type A in Mn(c) if it satisfies R��ϕ = ϕR�� and at the same time R��(Sϕ - ϕS) = 0.
Keywords
real hypersurface; structure Jacobi operator; Ricci tensor; Hopf hypersurface;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 J. Berndt, Real hypersurfaces with constant principal curvatures in complex hyperbolic space, 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.   DOI
3 J. T. Cho and U-H. Ki, Real hypersurfaces in complex projective space in terms of Jacobi operators, Acta Math. Hungar., 80(1998), 155-167.   DOI
4 U-H. Ki, S. J. Kim, and S.-B. Lee, The structure Jacobi operator on real hypersurfaces in a nonflat complex space form, Bull. Korean Math. Soc., 42(2005), 337-358.   DOI
5 U-H. Ki, I.-B. Kim and D. H. Lim, Characterizations of real hypersurfaces of type A in a complex space form, Bull. Korean Math. Soc., 47(2010), 1-15.   DOI
6 U-H. Ki, S. Nagai and R. Takagi, Real hypersurfaces in nonflat complex space forms concerned with the structure Jacobi operator and Ricci tensor, Topics in Almost Hermitian Geometry and Related Fields, 140-156, World Scientific, 2005.
7 U-H. Ki, S. Nagai and R. Takagi, Structure Jacobi opertor of real hypersurfaces with constant scalar curvature in a nonflat complex space form, Tokyo J. Math., 30(2007), 441-454.   DOI
8 U-H. Ki, S. Nagai and R. Takagi, The structure vector field and structure Jacobi operator of real hypersurfaces in nonflat complex space forms, Geom. Dedicata, 149(2010), 161-176.   DOI
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 M. Kimura, Real hypersurfaces and complex submanifolds in complex projective space, Trans. Amer. Math. Soc., 296(1986), 137-149.   DOI
11 S. Montiel and A. Romero, On some real hypersurfaces of a complex hyperbolic space, Geome. Dedicata, 20(1986), 245-261.   DOI
12 R. Niebergall and P. J. Ryan, Real hypersurfaces in complex space forms, Tight and Taut submanifolds, 233-305, Combridge Univ. Press, 1998.
13 M. Okumura, On some real hypersurfaces of a complex projective space, Trans. Amer. Math. Soc., 212(1975), 355-364.   DOI
14 R. Takagi, On homogeneous real hypersurfaces in a complex projective space, Osaka J. Math., 19(1973), 495-506.
15 R. Takagi, Real hypersurfaces in a complex projective space with constant principal curvatures I, II, J. Math. Soc. Japan, 27(1975), 43-53, 507-516.   DOI