Geodesic
Real Hypersurfaces in Complex Two-Plane Grassmannians with Generalized Tanaka–Webster Invariant Shape Operator
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013) no. 3, pp. 360-378 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, we introduce a new notion of the generalized Tanaka–Webster invariant for a hypersurface $M$ in $G_2(\mathbb{C}^{m+2})$, and give a non-existence theorem for Hopf hypersurfaces in $G_2(\mathbb{C}^{m+2})$ with generalized Tanaka–Webster invariant shape operator. 
@article{JMAG_2013_9_3_a4,
     author = {I. Jeong and E. Pak and Y. J. Suh},
     title = {Real {Hypersurfaces} in {Complex} {Two-Plane} {Grassmannians} with {Generalized} {Tanaka{\textendash}Webster} {Invariant} {Shape} {Operator}},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {360--378},
     year = {2013},
     volume = {9},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a4/}
}
TY  - JOUR
AU  - I. Jeong
AU  - E. Pak
AU  - Y. J. Suh
TI  - Real Hypersurfaces in Complex Two-Plane Grassmannians with Generalized Tanaka–Webster Invariant Shape Operator
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2013
SP  - 360
EP  - 378
VL  - 9
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a4/
LA  - en
ID  - JMAG_2013_9_3_a4
ER  - 
%0 Journal Article
%A I. Jeong
%A E. Pak
%A Y. J. Suh
%T Real Hypersurfaces in Complex Two-Plane Grassmannians with Generalized Tanaka–Webster Invariant Shape Operator
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2013
%P 360-378
%V 9
%N 3
%U http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a4/
%G en
%F JMAG_2013_9_3_a4
I. Jeong; E. Pak; Y. J. Suh. Real Hypersurfaces in Complex Two-Plane Grassmannians with Generalized Tanaka–Webster Invariant Shape Operator. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013) no. 3, pp. 360-378. http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a4/

[1] D. V. Alekseevskii, “Compact Quaternion Spaces”, Funct. Anal. Appl., 2 (1968), 106–114 | DOI | MR

[2] J. Berndt, “Riemannian Geometry of Complex Two-Plane Grassmannian”, Rend. Sem. Mat. Univ. Politec. Torino, 55 (1997), 19–83 | MR | Zbl

[3] J. Berndt, Y. J. Suh, “Real Hypersurfaces in Complex Two-Plane Grassmannians”, Monatshefte für Math., 127 (1999), 1–14 | DOI | MR | Zbl

[4] J. Berndt, Y. J. Suh, “Isometric Flows on Real Hypersurfaces in Complex Two-Plane Grassmannians”, Monatshefte für Math., 137 (2002), 87–98 | DOI | MR | Zbl

[5] I. Jeong, H. Lee, Y. J. Suh, “Real Hypersurfaces in Complex Two-Plane Grassmannians with Generalized Tanaka–Webster Parallel Shape Operator”, Kodai Math. J., 34 (2011), 352–366 | DOI | MR | Zbl

[6] I. Jeong, M. Kimura, H. Lee, Y. J. Suh, “Real Hypersurfaces in Complex Two-Plane Grassmannians with Generalized Tanaka–Webster Reeb Parallel Shape Operator”, Montshefte für Math., 172 (2013) (to appear)

[7] I. Jeong, H. Lee, Y. J. Suh, “Real Hypersurfaces in Complex Two-Plane Grassmannians with Generalized Tanaka–Webster $\mathfrak{D}^\perp$-parallel Shape Operator”, Int. J. Geom. Methods in Modern Physics, 9:4 (2012), 1250032, 20 pp. | DOI | MR | Zbl

[8] I. Jeong, C. J. G. Machado, J. D. Pérez, Y. J. Suh, “Real Hypersurfaces in Complex Two-Plane Grassmannians with $\mathfrak{D}^\perp$-parallel Structure Jacobi Operator”, Int. J. Math., 22:5 (2011), 655–673 | DOI | MR | Zbl

[9] M. Kon, “Real Hypersurfaces in Complex Space Forms and the Generalized Tanaka–Webster Connection”, Proc. of the 13th International Workshop on Differential Geometry and Related Fields, eds. Y. J. Suh, J. Berndt, Y. S. Choi, NIMS, 2009, 145–159 | MR

[10] H. Lee, Y. J. Suh, “Real Hypersurfaces of type $B$ in Complex Two-Plane Grassmannians Related to the Reeb Vector”, Bull. Korean Math. Soc., 47:3 (2010), 551–561 | DOI | MR | Zbl

[11] J. D. Pérez, Y. J. Suh, “The Ricci Tensor of Real Hypersurfaces in Complex Two-Plane Grassmannians”, J. Korean Math. Soc., 44 (2007), 211–235 | DOI | MR | Zbl

[12] Y. J. Suh, “Real Hypersurfaces in Complex Two-Plane Grassmannians with Parallel Shape Operator”, Bull. Austral. Math. Soc., 68 (2003), 493–502 | DOI | MR

[13] Y. J. Suh, “Real Hypersurfaces in Complex Two-Plane Grassmannians with Parallel Shape Operator, II”, J. Korean Math. Soc., 41 (2004), 535–565 | DOI | MR | Zbl

[14] Y. J. Suh, “Real Hypersurfaces in Complex Two-Plane Grassmannians with Vanishing Lie Derivative”, Canad. Math. Bull., 49 (2006), 134–143 | DOI | MR | Zbl

[15] N. Tanaka, “On Non-Degenerate Real Hypersurfaces, Graded Lie Algebras and Cartan Connections”, Japan J. Math., 20 (1976), 131–190 | MR

[16] S. Tanno, “Variational Problems on Contact Riemannian Manifolds”, Trans. Amer. Math. Soc., 314:1 (1989), 349–379 | DOI | MR | Zbl

[17] S. M. Webster, “Pseudo-Hermitian Structures on a Real Hypersurface”, J. Diff. Geom., 13 (1978), 25–41 | MR | Zbl