Abbena, Elsa An example of an almost Kähler manifold which is not Kählerian. (English) Zbl 0559.53023 Boll. Unione Mat. Ital., VI. Ser., A 3, 383-392 (1984). The author introduces a 4-dimensional compact homogeneous space \(M=G/\Gamma\) where G is a certain connected Lie group and \(\Gamma\) a discrete subgroup. A metric and a compact almost complex structure are defined on M. It is possible to prove that M is the homogeneous space corresponding to the manifold defined by W. Thurston [Proc. Am. Math. Soc. 55, 467-468 (1976; Zbl 0324.53031)]. This manifold is shown to be an almost Kähler manifold which is not Kählerian. Finally the author studies the curvature of M. Reviewer: S.S.Singh Cited in 14 Documents MSC: 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C30 Differential geometry of homogeneous manifolds Keywords:homogeneous space; almost complex structure; almost Kähler manifold PDF BibTeX XML Cite \textit{E. Abbena}, Boll. Unione Mat. Ital., VI. Ser., A 3, 383--392 (1984; Zbl 0559.53023)