HOPF HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH LIE PARALLEL NORMAL JACOBI OPERATOR

Title & Authors
HOPF HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH LIE PARALLEL NORMAL JACOBI OPERATOR
Jeong, Im-Soon; Lee, Hyun-Jin; Suh, Young-Jin;

Abstract
In this paper we give some non-existence theorems for Hopf hypersurfaces in the complex two-plane Grassmannian $\small{G_2(\mathbb{C}^{m+2})}$ with Lie parallel normal Jacobi operator $\small{\bar{R}_N}$ and totally geodesic D and $\small{D^{\bot}}$ components of the Reeb flow.
Keywords
complex two-plane Grassmannians;Hopf hypersurfaces;Reeb vector field;normal Jacobi operator;Lie derivative;
Language
English
Cited by
1.
RECURRENT JACOBI OPERATOR OF REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS,;;;

대한수학회보, 2013. vol.50. 2, pp.525-536
1.
Semi-parallelism of normal Jacobi operator for Hopf hypersurfaces in complex two-plane Grassmannians, Monatshefte für Mathematik, 2013, 172, 2, 167
2.
RECURRENT JACOBI OPERATOR OF REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS, Bulletin of the Korean Mathematical Society, 2013, 50, 2, 525
References
1.
J. Berndt, Real hypersurfaces in quaternionic space forms, J. Reine Angew. Math. 419 (1991), 9-26.

2.
J. Berndt, Riemannian geometry of complex two-plane Grassmannians, Rend. Sem. Mat. Univ. Politec. Torino 55 (1997), no. 1, 19-83.

3.
J. Berndt and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians, Monatsh. Math. 127 (1999), no. 1, 1-14.

4.
J. Berndt and Y. J. Suh, Real hypersurfaces with isometric Reeb ow in complex two-plane Grassmannians, Monatsh. Math. 137 (2002), no. 2, 87-98.

5.
I. Jeong, H. J. Kim, and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with parallel normal Jacobi operator, Publ. Math. Debrecen 76 (2010), no. 1-2, 203-218.

6.
I. Jeong and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with Lie ${\varepsilon}-parallel$ normal Jacobi operator, J. Korean Math. Soc. 45 (2008), no. 4, 1113-1133.

7.
H. Lee, J. D. Perez, F. G. Santos, and Y. J. Suh, On the structure Jacobi operator of a real hypersurface in complex projective space, Monatsh. Math. 158 (2009), no. 2, 187-194.

8.
J. D. Perez, I. Jeong, and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with commuting normal Jacobi operator, Acta Math. Hungar. 117 (2007), no. 3, 201-217.

9.
J. D. Perez, F. G. Santos, and Y. J. Suh, Real hypersurfaces in complex projective space whose structure Jacobi operator is Lie ${\varepsilon}-parallel$, Differential Geom. Appl. 22 (2005), no. 2, 181-188.

10.
J. D. Perez and Y. J. Suh, Real hypersurfaces of quaternionic projective space satisfying ${\nabla}_{U_R}$ = 0, Differential Geom. Appl. 7 (1997), no. 3, 211-217.

11.
J. D. Perez and Y. J. Suh, The Ricci tensor of real hypersurfaces in complex two-plane Grassmannians, J. Korean Math. Soc. 44 (2007), no. 1, 211-235.

12.
Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator, Bull. Austral. Math. Soc. 67 (2003), no. 3, 493-502.

13.
Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with commuting shape operator, Bull. Austral. Math. Soc. 68 (2003), no. 3, 379-393.

14.
Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator II, J. Korean Math. Soc. 41 (2004), no. 3, 535-565.

15.
Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with vanishing Lie derivatives, Canad. Math. Bull. 49 (2006), no. 1, 134-143.