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.
Hyunjin Lee, Young Jin Suh, Changhwa Woo
Kyungpook National University; Kyungpook National University; Pukyong National University
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.
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