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/