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.
@article{bwmeta1.element.doi-10_1515_math-2015-0032,
author = {Konstantina Panagiotidou and Juan de Dios P\'erez},
title = {Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms},
journal = {Open Mathematics},
volume = {13},
year = {2015},
zbl = {1329.53078},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0032}
}
Konstantina Panagiotidou; Juan de Dios Pérez. Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0032/
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