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An example of an almost Kähler manifold which is not Kählerian. (English) Zbl 0559.53023
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

##### MSC:
 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C30 Differential geometry of homogeneous manifolds