We study 4-dimensional Einstein-Hermitian non-Kähler manifolds admitting a certain anti-Hermitian structure. We also describe Einstein 4-manifolds which are of cohomogeneity 1 with respect to an at least 4-dimensional group of isometries.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap81-1-2, author = {W\l odzimierz Jelonek}, title = {Einstein-Hermitian and anti-Hermitian 4-manifolds}, journal = {Annales Polonici Mathematici}, volume = {81}, year = {2003}, pages = {7-24}, zbl = {1031.53041}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap81-1-2} }
Włodzimierz Jelonek. Einstein-Hermitian and anti-Hermitian 4-manifolds. Annales Polonici Mathematici, Tome 81 (2003) pp. 7-24. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap81-1-2/