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

Abbena, Elsa

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

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