Geodesic
Lie Invariant Shape Operator for Real Hypersurfaces in Complex Two-Plane Grassmannians~II
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013), pp. 455-475.

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A new notion of the generalized Tanaka–Webster $\mathfrak D^{\bot}$-invariant for a hypersurface $M$ in $G_2({\mathbb C}^{m+2})$ is introduced, and a classification of Hopf hypersurfaces in $G_2({\mathbb C}^{m+2})$ with generalized Tanaka–Webster $\mathfrak D^{\bot}$-invariant shape operator is given. 
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I. Jeong; E. Pak; Y. J. Suh. Lie Invariant Shape Operator for Real Hypersurfaces in Complex Two-Plane Grassmannians~II. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013), pp. 455-475. http://geodesic.mathdoc.fr/item/JMAG_2013_9_a2/

[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, H. Lee, M. Kimura, Y. J. Suh, “Real Hypersurfaces in Complex Two-Plane Grassmannians with Generalized Tanaka–Webster Reeb Parallel Shape Operator”, Monatshefte für Math., 170 (2013) (to appear) | MR

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

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

[9] I. Jeong, E. Pak, Y. J. Suh, “Real Hypersurfaces in Complex Two-Plane Grassmannians with Generalized Tanaka–Webster Invariant Shape Operator”, J. Math. Phys., Anal., Geom., 9:3 (2013), 360–378 | Zbl

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

[11] 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

[12] 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

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

[14] 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

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

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

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

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