It is proved that there exists a non-semisymmetric pseudosymmetric Kähler manifold of dimension 4.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-2-3, author = {Zbigniew Olszak}, title = {On the existence of pseudosymmetric K\"ahler manifolds}, journal = {Colloquium Mathematicae}, volume = {96}, year = {2003}, pages = {185-189}, zbl = {1045.53020}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-2-3} }
Zbigniew Olszak. On the existence of pseudosymmetric Kähler manifolds. Colloquium Mathematicae, Tome 96 (2003) pp. 185-189. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-2-3/