Abstract
In this paper, we have considered new commuting conditions, that is, (R ξ ϕ)S = S(R ξ ϕ) (resp. \((\bar{R}_{N}\phi )S = S(\bar{R}_{N}\phi )\)) between the Jacobi operators R ξ (resp. \(\bar{R}_{N}\)), the structure tensor field ϕ and the Ricci tensor S for real hypersurfaces M in \(G_{2}(\mathbb{C}^{m+2})\). With such a condition we give a complete classification of Hopf hypersurfaces M in \(G_{2}(\mathbb{C}^{m+2})\).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alekseevskii, D.V.: Compact quaternion spaces. Funct. Anal. Appl. 2, 106–114 (1968)
Berndt, J., Suh, Y.J.: Real hypersurfaces in complex two-plane Grassmannians. Monatsh. Math. 127, 1–14 (1999)
Berndt, J., Suh, Y.J.: Real hypersurfaces with isometric Reeb flow in complex two-plane Grassmannians. Monatsh. Math. 137, 87–98 (2002)
Jeong, I., Machado, C.J.G., Pérez, J.D., Suh, Y.J.: Real hypersurfaces in complex two-plane Grassmannians with \(\mathfrak{D}^{\perp }\)-parallel structure Jacobi operator. Int. J. Math. 22, 655–673 (2011)
Lee, H., Suh, Y.J.: Real hypersurfaces of type B in complex two-plane Grassmannians related to the Reeb vector. Bull. Korean Math. Soc. 47, 551–561 (2010)
Pérez, J.D., Suh, Y.J.: The Ricci tensor of real hypersurfaces in complex two-plane Grassmannians. J. Korean Math. Soc. 44, 211–235 (2007)
Pérez, J.D., Jeong, I., Suh, Y.J.: Real hypersurfaces in complex two-plane Grassmannians with commuting normal Jacobi operator. Acta Math. Hungar. 117, 201–217 (2007)
Suh, Y.J.: Real hypersurfaces in complex two-plane Grassmannians with commuting Ricci tensor. J. Geom. Phys. 60, 1792–1805 (2010)
Suh, Y.J., Yang, H.Y.: Real hypersurfaces in complex two-plane Grassmannians with commuting structure Jacobi operator. Bull. Korean Math. Soc. 45, 495–507 (2008)
Acknowledgements
This work was supported by Grant Proj. No. NRF-2011-220-C00002 from National Research Foundation of Korea. The first author by Grant Proj. No. NRF-2012- R1A2A2A01043023 and the third author supported by NRF Grant funded by the Korean Government (NRF-2013-Fostering Core Leaders of Future Basic Science Program).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Japan
About this paper
Cite this paper
Pak, E., Suh, Y.J., Woo, C. (2014). Real Hypersurfaces in Complex Two-Plane Grassmannians with Commuting Jacobi Operators. In: Suh, Y.J., Berndt, J., Ohnita, Y., Kim, B.H., Lee, H. (eds) Real and Complex Submanifolds. Springer Proceedings in Mathematics & Statistics, vol 106. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55215-4_16
Download citation
DOI: https://doi.org/10.1007/978-4-431-55215-4_16
Published:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-55214-7
Online ISBN: 978-4-431-55215-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)