G. Machado, Carlos J. et al., Commuting structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians, Acta mathematica Sinica. English series (Print) , 31(1), 2015, pp. 111-122
We classify real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator commutes either with any other Jacobi operator or with the normal Jacobi operator.