ON CHARACTERIZATIONS OF REAL HYPERSURFACES WITH ${\eta}-PARALLEL$ RICCI OPERATORS IN A COMPLEX SPACE FORM

Title & Authors
ON CHARACTERIZATIONS OF REAL HYPERSURFACES WITH ${\eta}-PARALLEL$ RICCI OPERATORS IN A COMPLEX SPACE FORM
Kim, In-Bae; Park, Hye-Jeong; Sohn, Woon-Ha;

Abstract
We shall give a characterization of a real hypersurface M in a complex space form Mn(c), $\small{c\;{\neq}\;0}$, whose Ricci operator and structure tensor commute each other on the holomorphic distribution of M, and the Ricci operator is $\small{{\eta}-parallel}$.
Keywords
real hypersurfaces;model spaces of type A or B;
Language
English
Cited by
1.
CHARACTERIZATIONS OF REAL HYPERSURFACES OF COMPLEX SPACE FORMS IN TERMS OF RICCI OPERATORS,;

대한수학회보, 2007. vol.44. 1, pp.195-202
1.
A study of real hypersurfaces with Ricci operators in 2-dimensional complex space forms, Pacific Journal of Mathematics, 2013, 266, 2, 305
References
1.
C. Baikoussis, A characterization of real hypersurfaces in complex space forms in terms of the Ricci tensor, Canad. Math. Bull. 40 (1997), no. 3, 257-265

2.
J. Berndt, Real hypersurfaces with constant principal curvatures in complex hy- perbolic space, J. Reine Angew Math. 395 (1989), 132-141

3.
M. Kimura and S. Maeda, On real hypersurfaces of a complex projective space, Math. Z. 202 (1989), no. 3, 299-311

4.
M. Kimura and S. Maeda, Characterizations of geodesic hyperspheres in a complex projective space in terms of Ricci tensors, Yokohama Math. J. 40 (1992), no. 1, 35-43

5.
R. Niebergall and P. J. Ryan, Real hypersurfaces in complex space forms: in Tight and taut submanifolds,, Math. Sci. Res. Inst. Publ., 32., 233-305 Publications, Cambridge, 1997

6.
Y. J. Suh, On real hypersurfaces of a complex space form with $\eta$-parallel Ricci tensor, Tsukuba J. Math. 14 (1990), no. 1, 27-37

7.
R. Takagi, On homogeneous real hypersurfaces in a complex projective space, Osaka J. Math. 10 (1973), 495-506

8.
R. Takagi, I. -B. Kim and B. H. Kim, The rigidity for real hypersurfaces in a complex projective space, Tohoku Math. J. (2) 50 (1998), no. 4, 531-536

9.
T. Taniguchi, Characterizations of real hypersurfaces of a complex hyperbolic space in terms of Ricci tensor and holomorphic distribution, Tsukuba J. Math. 18 (1994), no. 2, 469-482