Czechoslovak Mathematical Journal, online first, 16 pp.

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.

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

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 2010): 53C40, 53C15

DOI: 10.21136/CMJ.2017.0289-16

Full text available as PDF.


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