Real hypersurfaces with Reeb Jacobi operator of Codazzi type in the complex hyperbolic two-plane Grassmannians

Utilizing the concept of Reeb Jacobi operator of Codazzi type, we investigate Hopf real hypersurfaces in the complex hyperbolic two-plane Grassmannian $G^{*}_2(\mathbb {C}^{m+2})$ which admit a constant Reeb function α along the Reeb direction of ξ. If the Reeb function α is constant along the Reeb direction, then the Reeb vector field $\xi =-JN$ either belongs to the distribution ${\mathfrak D}$ or the distribution ${\mathfrak D}^{\bot }$. By virtue of this fact, we have proved a new result about Reeb Jacobi operator of Codazzi type according to the Reeb vector field $\xi \in \mathfrak {D}^{\bot }$ or $\xi \in \mathfrak {D}$, respectively.