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 Generalized Killing structure Jacobi operator for real hypersurfaces in complex hyperbolic two-plane Grassmannians J. Korean Math. Soc.Published online August 30, 2021 Hyunjin Lee, Young Jin Suh, and 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 : 53C40; 53C15. Full-Text :