Real Hypersurfaces in Complex Hyperbolic Space with Commuting Ricci Tensor

• Journal title : Kyungpook mathematical journal
• Volume 48, Issue 3,  2008, pp.433-442
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2008.48.3.433
Title & Authors
Real Hypersurfaces in Complex Hyperbolic Space with Commuting Ricci Tensor
Ki, U-Hang; Suh, Young-Jin;

Abstract
In this paper we consider a real hypersurface M in complex hyperbolic space $\small{H_n\mathbb{C}}$ satisfying $\small{S{\phi}A\;=\;{\phi}AS}$, where $\small{\phi}$, A and S denote the structure tensor, the shape operator and the Ricci tensor of M respectively. Moreover, we give a characterization of real hypersurfaces of type A in $\small{H_n\mathbb{C}}$ by such a commuting Ricci tensor.
Keywords
real hypersurface;Ricci tensor;Hopf hypersurface;
Language
English
Cited by
1.
Real Hypersurfaces in Complex Two-plane Grassmannians with F-parallel Normal Jacobi Operator,;;

Kyungpook mathematical journal, 2011. vol.51. 4, pp.395-410
1.
Real Hypersurfaces in Complex Two-plane Grassmannians with F-parallel Normal Jacobi Operator, Kyungpook mathematical journal, 2011, 51, 4, 395
References
1.
J. Berndt, Real hypersurfaces with constant principal curvatures in a complex hyperbolic space, J. Reine Agnew. 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.-H. Kwon and Y.J. Suh, A new characterization of homogeneous real hypersurfaces in complex space forms, Nihonkai Math. J. 9(1998), 77-90.

4.
M. Kimura, Real hypersurfaces and complex submanifolds in complex projective space, Trans. Amer. Math. Soc. 296(1986), 137-149.

5.
M. Kimura and S. Maeda, Lie derivatives on real hypersurfaces in a complex projective space, Czechoslovak Math. J. 45(1995), 135-148.

6.
M. Lohnherr and H. Reckziegel, On ruled real hypersurfaces in complex space forms, Geom. Dedicata 74(1999), 267-286.

7.
S. Montiel and A. Romero, On some real hypersurfaces of a complex hyperbolic space, Geom. Dedicata 20(1986), 245-261.

8.
R. Takagi, On homogeneous real hypersurfaces in a complex projective space, Osaka J. Math. 10(1973), 495-506.