Nonexistence of 4-dimensional almost Kaehler manifolds of constant curvature

Blair, David E.

doi:10.1090/S0002-9939-1990-1043404-2

Nonexistence of $4$-dimensional almost Kaehler manifolds of constant curvature
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Proc. Amer. Math. Soc. 110 (1990), 1033-1039 Request permission

Abstract:

It is shown that in dimension 4 there are no almost Kaehler manifolds of constant curvature unless the constant is 0, in which case the manifold is Kaehlerian. This was previously shown in dimensions $\geq 8$ by Z. Olszak and remains open in dimension 6.

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