Real hypersurfaces in complex two-plane Grassmannians with commuting restricted Jacobi operators

In this paper, we have considered a new commuting condition, that is, $(R_ξϕ) S = S (R_ξϕ)$ \big(resp. $(\Bar{R}_Nϕ) S = S (\Bar{R}_Nϕ$)\big) between the restricted Jacobi operator~$R_ξϕ$ (resp. $\Bar{R}_Nϕ$), and the Ricci tensor $S$ for real hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$. In terms of this condition we give a complete classification for Hopf hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$.

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