Browse > Article
http://dx.doi.org/10.4134/BKMS.2015.52.1.057

REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WHOSE SHAPE OPERATOR IS OF CODAZZI TYPE IN GENERALIZED TANAKA-WEBSTER CONNECTION  

Cho, Kyusuk (Department of Mathematics Kyungpook National University)
Lee, Hyunjin (The Center for Geometry and its Applications Pohang University of Science & Technology)
Pak, Eunmi (Department of Mathematics Kyungpook National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.1, 2015 , pp. 57-68 More about this Journal
Abstract
In this paper, we give a non-existence theorem of Hopf hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$, $m{\geq}3$, whose shape operator is of Codazzi type in generalized Tanaka-Webster connection $\hat{\nabla}^{(k)}$.
Keywords
complex two-plane Grassmannians; Hopf hypersurface; generalized Tanaka-Webster connection; shape operator; Codazzi type tensor;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 D. V. Alekseevskii, Compact quaternion spaces, Funct. Anal. Appl. 2 (1968), 106-114.   DOI
2 J. Berndt, Riemannian geometry of complex two-plane Grassmannian, Rend. Semin. 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.   DOI
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.   DOI
5 J. T. Cho, CR structures on real hypersurfaces of a complex space form, Publ. Math. Debrecen 54 (1999), no. 3-4, 473-487.
6 J. T. Cho and M. Kon, The Tanaka-Webster connection and real hypersurfaces in a complex space form, Kodai Math. J. 34 (2011), 474-484.   DOI   ScienceOn
7 I. Jeong, M. Kimura, H. Lee, and Y. J. Suh, Real hypersurfaces in complex twoplane Grassmannians with generalized Tanaka-Webster Reeb parallel shape operator, Monatsh. Math. 171 (2013), no. 3-4, 357-376.   DOI   ScienceOn
8 I. Jeong, H. Lee, and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel shape operator, Kodai Math. J. 34 (2011), no. 2, 352-366.   DOI   ScienceOn
9 I. Jeong, H. Lee, and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster ${\mathscr{D}^{\bot}}$-parallel shape operator, Int. J. Geom. Methods Mod. Phys. 9 (2012), no. 4, 1250032, 20 pp.
10 M. Kon, Real hypersurfaces in complex space forms and the generalized-Tanaka-Webster connection, Proceedings of the 13th International Workshop on Differential Geometry and Related Fields [Vol. 13], 145-159, Natl. Inst. Math. Sci. (NIMS), Daejeon 2009.
11 H. Lee and Y. J. Suh, Real hypersurfaces of type B in complex two-plane Grassmannians related to the Reeb vector, Bull. Korean Math. Soc. 47 (2010), no. 3, 551-561.   과학기술학회마을   DOI   ScienceOn
12 J. D. P'erez 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.   과학기술학회마을   DOI   ScienceOn
13 Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator, Bull. Aust. Math. Soc. 67 (2003), no. 3, 493-502.   DOI
14 N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Jpn. J. Math. 20 (1976), no. 1, 131-190.
15 S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc. 314 (1989), no. 1, 349-379.   DOI   ScienceOn
16 S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Differential Geom. 13 (1978), no. 1, 25-41.   DOI