REAL HYPERSURFACES OF TYPE B IN COMPLEX TWO-PLANE GRASSMANNIANS RELATED TO THE REEB VECTOR

Title & Authors
REAL HYPERSURFACES OF TYPE B IN COMPLEX TWO-PLANE GRASSMANNIANS RELATED TO THE REEB VECTOR
Lee, Hyun-Jin; Suh, Young-Jin;

Abstract
In this paper we give a new characterization of real hypersurfaces of type B, that is, a tube over a totally geodesic $\small{\mathbb{Q}P^n}$ in complex two-plane Grassmannians $\small{G_2(\mathbb{C}^{m+2})}$, where m
Keywords
complex two-plane Grassmannians;real hypersurfaces of type B;Hopf hypersurface;Reeb vector field;$\small{\mathfrak{D}}$-distribution;
Language
English
Cited by
1.
REAL HYPERSURFACES OF TYPE A IN COMPLEX TWO-PLANE GRASSMANNIANS RELATED TO THE NORMAL JACOBI OPERATOR,;;;

대한수학회보, 2012. vol.49. 2, pp.423-434
2.
RECURRENT JACOBI OPERATOR OF REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS,;;;

대한수학회보, 2013. vol.50. 2, pp.525-536
3.
REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WHOSE SHAPE OPERATOR IS OF CODAZZI TYPE IN GENERALIZED TANAKA-WEBSTER CONNECTION,;;;

대한수학회보, 2015. vol.52. 1, pp.57-68
1.
Real hypersurfaces in complex two-plane Grassmannians with harmonic curvature, Journal de Mathématiques Pures et Appliquées, 2013, 100, 1, 16
2.
Real Hypersurfaces in Complex Two-Plane Grassmannians Whose Jacobi Operators Corresponding to -Directions are of Codazzi Type, Advances in Pure Mathematics, 2011, 01, 03, 67
3.
Hopf Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Shape Operator, Bulletin of the Malaysian Mathematical Sciences Society, 2015, 38, 2, 617
4.
REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS SOME OF WHOSE JACOBI OPERATORS ARE ξ-INVARIANT, International Journal of Mathematics, 2012, 23, 03, 1250002
5.
Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition, Czechoslovak Mathematical Journal, 2012, 62, 3, 849
6.
Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster $$\mathfrak{D}^ \bot$$-parallel structure Jacobi operator, Open Mathematics, 2014, 12, 12
7.
Pseudo anti-commuting and Ricci soliton real hypersurfaces in complex two-plane Grassmannians, Journal of Geometry and Physics, 2014, 86, 258
8.
REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH GENERALIZED TANAKA–WEBSTER 𝔇⊥-PARALLEL SHAPE OPERATOR, International Journal of Geometric Methods in Modern Physics, 2012, 09, 04, 1250032
9.
Semi-parallel real hypersurfaces in complex two-plane Grassmannians, Differential Geometry and its Applications, 2014, 34, 87
10.
Levi-Civita and generalized Tanaka–Webster covariant derivatives for real hypersurfaces in complex two-plane Grassmannians, Annali di Matematica Pura ed Applicata (1923 -), 2015, 194, 3, 919
11.
REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WHOSE SHAPE OPERATOR IS OF CODAZZI TYPE IN GENERALIZED TANAKA-WEBSTER CONNECTION, Bulletin of the Korean Mathematical Society, 2015, 52, 1, 57
12.
Real Hypersurfaces in Complex Two-Plane Grassmannians with GTW Reeb Lie Derivative Structure Jacobi Operator, Mediterranean Journal of Mathematics, 2016, 13, 3, 1263
13.
REAL HYPERSURFACES OF TYPE A IN COMPLEX TWO-PLANE GRASSMANNIANS RELATED TO THE NORMAL JACOBI OPERATOR, Bulletin of the Korean Mathematical Society, 2012, 49, 2, 423
14.
Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator, Czechoslovak Mathematical Journal, 2015, 65, 1, 207
15.
Real hypersurfaces of complex two-plane Grassmannians with certain parallel conditions, Journal of Geometry, 2017
16.
Real hypersurfaces in complex two-plane Grassmannians with Reeb parallel Ricci tensor, Journal of Geometry and Physics, 2013, 64, 1
17.
Ricci Semi-symmetric Hypersurfaces in Complex Two-Plane Grassmannians, Bulletin of the Malaysian Mathematical Sciences Society, 2017, 40, 3, 1277
18.
Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster D-parallel shape operator, Acta Mathematica Sinica, English Series, 2017, 33, 1, 61
19.
Real Hypersurfaces in Complex Two-plane Grassmannians with $${\mathfrak{D}^{\bot}}$$ -Parallel Shape Operator, Results in Mathematics, 2013, 64, 3-4, 331
20.
Hopf Hypersurfaces in Complex Grassmannians of Rank Two, Results in Mathematics, 2017, 71, 3-4, 1083
21.
Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition II, Czechoslovak Mathematical Journal, 2014, 64, 1, 133
22.
Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians, Czechoslovak Mathematical Journal, 2015, 65, 2, 569
23.
Semi-parallelism of normal Jacobi operator for Hopf hypersurfaces in complex two-plane Grassmannians, Monatshefte für Mathematik, 2013, 172, 2, 167
24.
Real hypersurfaces in complex two-plane Grassmannians with recurrent Ricci tensor, International Journal of Geometric Methods in Modern Physics, 2015, 12, 09, 1550086
25.
RECURRENT JACOBI OPERATOR OF REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS, Bulletin of the Korean Mathematical Society, 2013, 50, 2, 525
26.
Real hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster Reeb parallel shape operator, Monatshefte für Mathematik, 2013, 171, 3-4, 357
27.
Semi-parallel symmetric operators for Hopf hypersurfaces in complex two-plane Grassmannians, Monatshefte für Mathematik, 2015, 177, 4, 539
28.
On the Riemannian Curvature Tensor of a Real Hypersurface in Complex Two-Plane Grassmannians, Bulletin of the Malaysian Mathematical Sciences Society, 2017
References
1.
J. Berndt, Riemannian geometry of complex two-plane Grassmannians, Rend. Sem. Mat. Univ. Politec. Torino 55 (1997), no. 1, 19-83.

2.
J. Berndt, Real hypersurfaces with constant principal curvatures in complex space forms, Proceedings of the Tenth International Workshop on Differential Geometry, 1–2, Kyungpook Nat. Univ., Taegu, 2006.

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 flow in complex two-plane Grassmannians, Monatsh. Math. 137 (2002), no. 2, 87–98.

5.
T. E. Cecil and P. J. Ryan, Focal sets and real hypersurfaces in complex projective space, Trans. Amer. Math. Soc. 269 (1982), no. 2, 481-499.

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

7.
M. Kimura, Real hypersurfaces and complex submanifolds in complex projective space, Trans. Amer. Math. Soc. 296 (1986), no. 1, 137-149.

8.
Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with commuting shape operator, Bull. Austral. Math. Soc. 68 (2003), no. 3, 379-393.

9.
Y. J. Suh, Real hypersurfaces of type B in complex two-plane Grassmannians, Monatsh. Math. 147 (2006), no. 4, 337-355.

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

11.
K. Yano and M. Kon, CR Submanifolds of Kaehlerian and Sasakian Manifolds, Progress in Mathematics, 30. Birkhauser, Boston, Mass., 1983.