Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2022; 59(2): 255-278

Online first article February 11, 2022      Printed March 1, 2022

https://doi.org/10.4134/JKMS.j200614

Copyright © The Korean Mathematical Society.

Generalized Killing structure Jacobi operator for real hypersurfaces in complex hyperbolic two-plane Grassmannians

Hyunjin Lee, Young Jin Suh, Changhwa Woo

Kyungpook National University; Kyungpook National University; Pukyong National University

Abstract

In this paper, first we introduce a new notion of generalized Killing structure Jacobi operator for a real hypersurface $M$ in complex hyperbolic two-plane Grassmannians $S U_{2, m} / S\left(U_{2} \cdot U_{m}\right)$. Next we prove that there does not exist a Hopf real hypersurface in complex hyperbolic two-plane Grassmannians $S U_{2, m} / S\left(U_{2} \cdot U_{m}\right)$ with generalized Killing structure Jacobi operator.

Keywords: Generalized Killing structure Jacobi operator, cyclic parallel structure Jacobi operator, geodesic Reeb flow, Hopf hypersurface

MSC numbers: Primary 53C40; Secondary 53C15

Supported by: This work was supported by grant Proj. No. NRF-2020-R1A2C1A-01101518 from National Research Foundation of Korea. The first author was supported by grant Proj. No. NRF-2019-R1I1A1A-01050300, the second author was supported by grant Proj. No. NRF-2018-R1D1A1B-05040381 and the third author was supported by the Pukyong National University Research Fund in 2019.