We prove that every compact balanced astheno-Kähler manifold is Kähler, and that there exists an astheno-Kähler structure on the product of certain compact normal almost contact metric manifolds.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm89-2-6, author = {Koji Matsuo and Takao Takahashi}, title = {On compact astheno-K\"ahler manifolds}, journal = {Colloquium Mathematicae}, volume = {89}, year = {2001}, pages = {213-221}, zbl = {1032.53018}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm89-2-6} }
Koji Matsuo; Takao Takahashi. On compact astheno-Kähler manifolds. Colloquium Mathematicae, Tome 89 (2001) pp. 213-221. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm89-2-6/