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Examples of non-Kähler, almost Kähler symmetric spaces. (English) Zbl 0877.53032

The author and the reviewer have constructed an example of strictly almost Kähler structure on the Riemannian product of a 3-dimensional hyperbolic space and a real line [T. Oguro and K. Sekigawa, Tsukuba J. Math. 20, No. 1, 151-161 (1996; MR 97e:53057)]. However, there are no known examples of strictly almost Kähler symmetric spaces of dimension \(\geq 6\).
In the present article, the author constructs uncountably many strictly almost Kähler structures on the Riemann product of 3-dimensional hyperbolic space and a \((2n-3)\)-dimensional Euclidean space, where \(2n\geq 6\).

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C35 Differential geometry of symmetric spaces
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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