Abstract
In this paper, we introduce a new commuting condition between the structure Jacobi operator and symmetric (1,1)-type tensor field T, that is, \({R_{\xi} \phi T = TR_{\xi} \phi}\), where T = A or T = S for Hopf hypersurfaces in complex hyperbolic two-plane Grassmannians. Using simultaneous diagonalization for commuting symmetric operators, we give a complete classification of real hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting condition, respectively.
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