Browse > Article
http://dx.doi.org/10.7468/jksmeb.2021.28.1.55

NON-EXISTANCE REAL HYPERSURFACES IN A NONFLAT COMPLEX SPACE FORM WITH CODAZZI TYPE OF STRUCTURE TENSOR FIELD  

Lim, Dong Ho (Department of Mathematics Education, Sehan University)
Kim, Hwa Soo (Department of Mathematics Education, Sehan University)
Publication Information
The Pure and Applied Mathematics / v.28, no.1, 2021 , pp. 55-60 More about this Journal
Abstract
Let M be a real hypersurface in a complex space form Mn(c), c ≠ 0. In this paper we prove that if the structure tensor field is Codazzi type, then M is a Hopf hypersurface. We characterize such Hopf hypersurfaces of Mn(c).
Keywords
Real hypersurface; Differential operator of structure tensor field; Hopf hypersurface; model spaces;
Citations & Related Records
Times Cited By KSCI : 1  (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 U-H. Ki & Y.J. Suh: On real hypersurfaces of a complex space form. J. Okayama Univ. 32 (1990), 207-221.
3 U-H. Ki, I.-B. Kim & D.H. Lim: Characterizations of real hypersurfaces of type A in a complex space form. Bull. Korean Math. Soc. 47 (2010), 1-15.   DOI
4 D.H. Lim: Characterizations of real hypersurfaces in a nonflat complex space form with respect to structure tensor field. Far East. J. Math. Scie. 104 (2018), 277-284.   DOI
5 S. Maeda & S. Udagawa: Real hypersurfaces of a complex projective space in terms of Holomorphic distribution. Tsukuba J. Math. 14 (1990), 39-52.
6 S. Montiel & A. Romero: On some real hypersurfaces of a complex hyperbolic space. Geometriae Dedicata. 20 (1986), 245-261.   DOI
7 R. Niebergall & P.J. Ryan: Real hypersurfaces in complex space forms in Tight and Taut submanifolds. Cambridge Univ. Press (1998), 233-305.
8 M. Okumura: On some real hypersurfaces of a complex projective space. Trans. Amer. Math. Soc. 212 (1975), 355-364.   DOI
9 M. Kimura & S. Maeda: On real hypersurfaces of a complex projective space. Math. Z. 202 (1989), 299-311.   DOI
10 R. Takagi: On homogeneous real hypersurfaces in a complex projective space. Osaka J. Math. 10 (1973), 495-506.