Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms Panagiotidou, Konstantina Pérez Jiménez, Juan De Dios Real hypersurfaces Structure Jacobi operator Cho operator Non-flat complex space forms In this paper three dimensional real hypersurfaces in non-flat complex space forms whose k-th Cho operator with respect to the structure vector field ξ commutes with the structure Jacobi operator are classified. Furthermore, it is proved that the only three dimensional real hypersurfaces in non-flat complex space forms, whose k-th Cho operator with respect to any vector field X orthogonal to structure vector field commutes with the structure Jacobi operator, are the ruled ones. Finally, results concerning real hypersurfaces in complex hyperbolic space satisfying the above conditions are also provided. 2015-10-22T10:25:08Z 2015-10-22T10:25:08Z 2015 info:eu-repo/semantics/article Panagiotidou, K.; Pérez Jiménez, J.D. Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms. Open Mathematics, 13(1): 321-332 (2015). [http://hdl.handle.net/10481/38572] 2391-5455 http://hdl.handle.net/10481/38572 10.1515/math-2015-0032 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ info:eu-repo/semantics/openAccess Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Gruyter Open