Czechoslovak Mathematical Journal, Vol. 67, No. 4, pp. 989-1004, 2017


Real hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting restricted normal Jacobi operators

Doo Hyun Hwang, Eunmi Pak, Changhwa Woo

Received June 7, 2016.   First published August 15, 2017.

Abstract:  We give a classification of Hopf real hypersurfaces in complex hyperbolic two-plane Grassmannians ${\rm SU}_{2,m}/S(U_2{\cdot}U_m)$ with commuting conditions between the restricted normal Jacobi operator $\overline{R}_N\phi$ and the shape operator $A$ (or the Ricci tensor $S$).
Keywords:  real hypersurface; complex hyperbolic two-plane Grassmannians; Hopf hypersurface; shape operator; Ricci tensor; normal Jacobi operator; commuting condition
Classification MSC:  53C40, 53C15
DOI:  10.21136/CMJ.2017.0289-16

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Affiliations:   Doo Hyun Hwang, Eunmi Pak, Department of Mathematics, Kyungpook National University, 80 Daehak-ro, Buk-gu, Daegu 702-701, Republic of Korea, e-mail: engus0322@knu.ac.kr, empak@knu.ac.kr; Changhwa Woo, Department of Mathematics Education, Woosuk University, 443 Samnyero, Samnye, 565-701 Wanju, Jeonbuk, Republic of Korea, e-mail: legalgwch@naver.com

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